Michielsen, K.; De Raedt, H.; Hess, K.
2011-03-28
We discuss the relation between Bell's and Boole's inequality. We apply both to the analysis of measurement results in idealized Einstein-Podolsky-Rosen-Bohm experiments. We present a local realist model that violates Bell's and Boole's inequality due to the absence of Boole's one-to-one correspondence between the two-valued variables of the mathematical description and the two-valued measurement results.
NASA Astrophysics Data System (ADS)
Chaves, Rafael
2016-01-01
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.
Lorentz-invariant Bell's inequality
Kim, Won Tae; Son, Edwin J.
2005-01-01
We study Bell's inequality in relation to the Einstein-Podolsky-Rosen paradox in the relativistic regime. For this purpose, a relativistically covariant analysis is used in the calculation of the Bell's inequality, which results in the maximally violated Bell's inequality in any reference frame.
Looking for symmetric Bell inequalities
NASA Astrophysics Data System (ADS)
Bancal, Jean-Daniel; Gisin, Nicolas; Pironio, Stefano
2010-09-01
Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.
Multisetting Bell inequality for qudits
NASA Astrophysics Data System (ADS)
Ji, Se-Wan; Lee, Jinhyoung; Lim, James; Nagata, Koji; Lee, Hai-Woong
2008-11-01
We propose a generalized Bell inequality for two three-dimensional systems with three settings in each local measurement. It is shown that this inequality is maximally violated if local measurements are configured to be mutually unbiased and a composite state is maximally entangled. This feature is similar to Clauser-Horne-Shimony-Holt inequality for two qubits but is in contrast with the two types of inequalities, Collins-Gisin-Linden-Massar-Popescu and Son-Lee-Kim, for high-dimensional systems. The generalization to aribitrary prime-dimensional systems is discussed.
Bell inequalities with communication assistance
NASA Astrophysics Data System (ADS)
Maxwell, Katherine; Chitambar, Eric
2014-04-01
In this paper, we consider the possible correlations between two parties using local machines and shared randomness with an additional amount of classical communication. This is a continuation of the work initiated by Bacon and Toner [Phys. Rev. Lett. 90, 157904 (2003), 10.1103/PhysRevLett.90.157904] who characterized the correlation polytope for 2×2 measurement settings with binary outcomes plus one bit of communication. Here, we derive a complete set of Bell inequalities for 3×2 measurement settings and a shared bit of communication. When the communication direction is fixed, nine Bell inequalities characterize the correlation polytope, whereas when the communication direction is bidirectional, 143 inequalities describe the correlations. We then prove a tight lower bound on the amount of communication needed to simulate all no-signaling correlations for a given number of measurement settings.
Compact Bell inequalities for multipartite experiments
NASA Astrophysics Data System (ADS)
Wu, Yu-Chun; Żukowski, Marek; Chen, Jing-Ling; Guo, Guang-Can
2013-08-01
A method for construction of multipartite Clauser-Horne-Shimony-Holt- (CHSH-) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. An iterative method for deriving (N+1)-partite CHSH-type Bell inequalities from N-partite ones is derived. As an application, compact Bell inequalities for eight observers involving just four correlation functions are proposed. They require much less experimental effort than standard methods and thus are experimentally friendly in multiphoton experiments.
A simple proof of Bell's inequality
NASA Astrophysics Data System (ADS)
Maccone, Lorenzo
2013-11-01
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an extremely simple proof of Bell's inequality; a single figure suffices. This simplicity may be useful in the unending debate over what exactly the Bell inequality means, because the hypotheses underlying the proof become transparent. It is also a useful didactic tool, as the Bell inequality can be explained in a single intuitive lecture.
Scalable Bell inequalities for multiqubit systems
NASA Astrophysics Data System (ADS)
He, Yingqiu; Ding, Dong; Yan, Fengli; Gao, Ting
2015-08-01
Based on Clauser-Horne-Shimony-Holt inequality, we show a fruitful method to exploit Bell inequalities for multipartite qubit systems. These Bell inequalities are designed with a simpler architecture tailored to experimental demonstration. With the point of view of the stabilizer formalism, we suggest a method to investigate quantum nonlocality for multipartite systems. Under the optimal setting we derive a set of compact Mermin-type inequalities and then discuss quantum violations for generalized Greenberger-Horne-Zeilinger (GGHZ) states and two kinds of mixed states. Also, as an example, we reveal relationship between quantum nonlocality and four-partite entanglement for four-qubit GGHZ states.
Bell inequalities resistant to detector inefficiency
Massar, Serge; Pironio, Stefano; Roland, Jeremie; Gisin, Bernard
2002-11-01
We derive both numerically and analytically Bell inequalities and quantum measurements that present enhanced resistance to detector inefficiency. In particular, we describe several Bell inequalities which appear to be optimal with respect to inefficient detectors for small dimensionality d=2,3,4 and two or more measurement settings at each side. We also generalize the family of Bell inequalities described by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)] to take into account the inefficiency of detectors. In addition, we consider the possibility for pairs of entangled particles to be produced with probability less than 1. We show that when the pair production probability is small, one should in general use different Bell inequalities than when the pair production probability is high.
Bell's inequality violation with spins in silicon
NASA Astrophysics Data System (ADS)
Dehollain, Juan P.; Simmons, Stephanie; Muhonen, Juha T.; Kalra, Rachpon; Laucht, Arne; Hudson, Fay; Itoh, Kohei M.; Jamieson, David N.; McCallum, Jeffrey C.; Dzurak, Andrew S.; Morello, Andrea
2016-03-01
Bell's theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity.
Bell's inequality violation with spins in silicon.
Dehollain, Juan P; Simmons, Stephanie; Muhonen, Juha T; Kalra, Rachpon; Laucht, Arne; Hudson, Fay; Itoh, Kohei M; Jamieson, David N; McCallum, Jeffrey C; Dzurak, Andrew S; Morello, Andrea
2016-03-01
Bell's theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity. PMID:26571006
Bell inequalities for quantum optical fields
NASA Astrophysics Data System (ADS)
Żukowski, Marek; Wieśniak, Marcin; Laskowski, Wiesław
2016-08-01
The commonly used "practical" Bell inequalities for quantum optical fields, which use intensities as the observables, are derivable only if specific additional assumptions hold. This limits the range of local hidden variable theories, which are invalidated by their violation. We present alternative Bell inequalities, which do not suffer from any (theoretical) loophole. The inequalities are for correlations of averaged products of local rates. By rates we mean ratios of the measured intensity in the given local output channel to the total local measured intensity, in the given run of the experiment. Bell inequalities of this type detect entanglement in situations in which the "practical" ones fail. Thus, we have full consistency with Bell's theorem, and better device-independent entanglement indicators. Strongly driven type-II parametric down conversion (bright squeezed vacuum) is our working example. The approach can be used to modify many types of standard Bell inequalities, to the case of undefined particle numbers. The rule is to replace the usual probabilities by rates.
Violation of Bell's inequalities in quantum optics
NASA Technical Reports Server (NTRS)
Reid, M. D.; Walls, D. F.
1984-01-01
An optical field produced by intracavity four-wave mixing is shown to exhibit the following nonclassical features: photon antibunching, squeezing, and violation of Cauchy-Schwarz and Bell's inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P function.
Relations between entanglement witnesses and Bell inequalities
Hyllus, Philipp; Guehne, Otfried; Bruss, Dagmar; Lewenstein, Maciej
2005-07-15
Bell inequalities, considered within quantum mechanics, can be regarded as nonoptimal witness operators. We discuss the relationship between such Bell witnesses and general entanglement witnesses in detail for the Bell inequality derived by Clauser, Horne, Shimony, and Holt (CHSH) [Phys. Rev. Lett. 23, 880 (1969)]. We derive bounds on how much an optimal witness has to be shifted by adding the identity operator to make it positive on all states admitting a local hidden variable model. In the opposite direction, we obtain tight bounds for the maximal proportion of the identity operator that can be subtracted from such a CHSH witness, while preserving the witness properties. Finally, we investigate the structure of CHSH witnesses directly by relating their diagonalized form to optimal witnesses of two different classes.
The probabilistic origin of Bell's inequality
NASA Technical Reports Server (NTRS)
Krenn, Guenther
1994-01-01
The concept of local realism entails certain restrictions concerning the possible occurrence of correlated events. Although these restrictions are inherent in classical physics they have never been noticed until Bell showed in 1964 that general correlations in quantum mechanics can not be interpreted in a classical way. We demonstrate how a local realistic way of thinking about measurement results necessarily leads to limitations with regard to the possible appearance of correlated events. These limitations, which are equivalent to Bell's inequality can be easily formulated as an immediate consequence of our discussion.
Generalized Bell-inequality experiments and computation
Hoban, Matty J.; Wallman, Joel J.; Browne, Dan E.
2011-12-15
We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich nonlocal box for many parties and nonbinary inputs and outputs at each site. Finally, we comment on the effect of preprocessing on measurement data in our generalized setting and show that it becomes problematic outside of the binary setting, in that it allows local hidden variable theories to simulate maximally nonlocal correlations such as those of these generalized Popescu-Rohrlich nonlocal boxes.
Entropy inequalities and Bell inequalities for two-qubit systems
Santos, Emilio
2004-02-01
Sufficient conditions for the nonviolation of the Bell-Clauser-Horne-Shimony-Holt inequalities in a mixed state of a two-qubit system are: (1) the linear entropy of the state is not smaller than 0.457; (2) the sum of the conditional linear entropies is not smaller than -0.086; (3) the von Neumann entropy is not smaller than 0.833; and (4) the sum of the conditional von Neumann entropies is not smaller than 0.280.
Better Bell-inequality violation by collective measurements
Liang, Y.-C.; Doherty, Andrew C.
2006-05-15
The standard Bell-inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.
Entanglement estimation from Bell inequality violation
NASA Astrophysics Data System (ADS)
Bartkiewicz, Karol; Horst, Bohdan; Lemr, Karel; Miranowicz, Adam
2013-11-01
It is well known that the violation of Bell's inequality in the form given by Clauser, Horne, Shimony, and Holt (CHSH) in two-qubit systems requires entanglement, but not vice versa, i.e., there are entangled states which do not violate the CHSH inequality. Here we compare some standard entanglement measures with violations of the CHSH inequality (as given by the Horodecki measure) for two-qubit states generated by Monte Carlo simulations. We describe states that have extremal entanglement according to the negativity, concurrence, and relative entropy of entanglement for a given value of the CHSH violation. We explicitly find these extremal states by applying the generalized method of Lagrange multipliers based on the Karush-Kuhn-Tucker conditions. The found minimal and maximal states define the range of entanglement accessible for any two-qubit states that violate the CHSH inequality by the same amount. We also find extremal states for the concurrence versus negativity by considering only such states which do not violate the CHSH inequality. Furthermore, we describe an experimentally efficient linear-optical method to determine the highest Horodecki degree of the CHSH violation for arbitrary mixed states of two polarization qubits. By assuming to have access simultaneously to two copies of the states, our method requires only six discrete measurement settings instead of nine settings, which are usually considered.
Avoiding loopholes with hybrid Bell-Leggett-Garg inequalities
NASA Astrophysics Data System (ADS)
Dressel, Justin; Korotkov, Alexander N.
2014-01-01
By combining the postulates of macrorealism with Bell locality, we derive a qualitatively different hybrid inequality that avoids two loopholes that commonly appear in Leggett-Garg and Bell inequalities. First, locally invasive measurements can be used, which avoids the "clumsiness" Leggett-Garg inequality loophole. Second, a single experimental ensemble with fixed analyzer settings is sampled, which avoids the "disjoint sampling" Bell inequality loophole. The derived hybrid inequality has the same form as the Clauser-Horne-Shimony-Holt Bell inequality; however, its quantum violation intriguingly requires weak measurements. A realistic explanation of an observed violation requires either the failure of Bell locality or a preparation conspiracy of finely tuned and nonlocally correlated noise. Modern superconducting and optical systems are poised to implement this test.
Avoiding Loopholes with Hybrid Bell-Leggett-Garg Inequalities
NASA Astrophysics Data System (ADS)
Dressel, Justin; Korotkov, Alexander
2014-03-01
By combining the postulates of macrorealism with Bell-locality, we derive a qualitatively different hybrid inequality that avoids two loopholes that commonly appear in Leggett-Garg and Bell inequalities. First, locally-invasive measurements can be used, which avoids the ``clumsiness'' Leggett-Garg inequality loophole. Second, a single experimental ensemble with fixed analyzer settings is sampled, which avoids the ``disjoint sampling'' Bell inequality loophole. The derived hybrid inequality has the same form as the Clauser-Horne-Shimony-Holt Bell inequality; however, its quantum violation intriguingly requires weak measurements. A realistic explanation of an observed violation requires either the failure of Bell-locality, or a preparation-conspiracy of finely tuned and nonlocally-correlated noise. Modern superconducting and optical implementations of this test are considered.
Bell's Inequalities, Superquantum Correlations, and String Theory
Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu; Tze, Chia-Hsiung
2011-01-01
We offermore » an interpretation of superquantum correlations in terms of a “doubly” quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tension α ' , and the string coupling constant g s , is such a superquantum theory that transgresses the usual quantum violations of Bell's inequalities. We also discuss the ℏ → ∞ limit of quantum mechanics in this context. As a superquantum theory, string theory should display distinct experimentally observable supercorrelations of entangled stringy states.« less
Proposed test for temporal Bell inequalities
Paz, J.P. ); Mahler, G. )
1993-11-15
Temporal Bell inequalities can be violated for sequences of events (histories) for which probabilities satisfying consistent sum rules cannot be defined. We discuss possible experiments in which such violations, never observed so far, may indeed be seen. The basic scheme, which uses three optically driven and mutually interacting two-level systems, could be implemented in a variety of nanostructures. It could even be mapped onto the dynamics of a single electron four-level system thus allowing for a realization in atomic physics.
Inequality by Design: Cracking the Bell Curve Myth [book review].
ERIC Educational Resources Information Center
Carroll, John B.
2002-01-01
This book, a critique of "The Bell Curve" by R. Herrnstein and C. Murray, explores what "inequality" in society means, how it arises, and how it can be measured or dealt with quantitatively. It also considers how societal and other variables work to increase or decrease inequality. The book argues that "The Bell Curve" vastly overestimates the…
Bell's inequality violation with non-negative Wigner functions
Revzen, M.; Mann, A.; Mello, P.A.; Johansen, L.M.
2005-02-01
A Bell inequality violation allowed by the two-mode squeezed state, whose Wigner function is nonnegative, is shown to hold only for correlations among dynamical variables that cannot be interpreted via a local hidden variable theory. Explicit calculations and interpretation are given for Bell's suggestion that the EPR (Einstein, Podolsky, and Rosen) state will not allow violation of Bell's inequality, in conjunction with its Wigner representative being nonnegative. It is argued that Bell's theorem disallowing the violation of Bell's inequality within a local hidden-variable theory depends on the dynamical variables having a definite value--assigned by the local hidden variables--even when they cannot be simultaneously measured. The analysis leads us to conclude that Bell's inequality violation is to be associated with endowing these definite values to the dynamical variables, and not with their locality attributes.
Experimental Bell-inequality violation without the postselection loophole
Lima, G.; Vallone, G.; Chiuri, A.; Cabello, A.; Mataloni, P.
2010-04-15
We report on an experimental violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality using energy-time-entangled photons. The experiment is not free of the locality and detection loopholes but is the first violation of the Bell-CHSH inequality using energy-time entangled photons which is free of the postselection loophole described by Aerts et al. [Phys. Rev. Lett. 83, 2872 (1999)].
Entanglement Measure and Quantum Violation of Bell-Type Inequality
NASA Astrophysics Data System (ADS)
Ding, Dong; He, Ying-Qiu; Yan, Feng-Li; Gao, Ting
2016-05-01
By calculating entanglement measures and quantum violation of Bell-type inequality, we reveal the relationship between entanglement measure and the amount of quantum violation for a family of four-qubit entangled states. It has been demonstrated that the Bell-type inequality is completely violated by these four-qubit entangled states. The plot of entanglement measure as a function of the expectation value of Bell operator shows that entanglement measure first decreases and then increases smoothly with increasing quantum violation.
Violation of Bell inequality in perfect translation-invariant systems
NASA Astrophysics Data System (ADS)
Sun, Zhao-Yu; Wu, Yu-Ying; Xu, Jian; Huang, Hai-Lin; Chen, Bo-Jun; Wang, Bo
2013-11-01
Bell inequalities and nonlocality have been widely studied in one-dimensional quantum systems. As a kind of quantum correlation, it is expected that bipartite nonlocality should be present in quantum systems, just as bipartite entanglement does. Surprisingly, for various models, two-qubit states do not violate Bell inequalities, i.e., they are local. Recently, it is realized that the results are related to the monogamy trade-off obeyed by bipartite Bell correlations, thus it is believed that for general translation invariant systems, two-qubit states should not violate the Bell inequality [Oliveira, Europhys. Lett.EULEEJ0295-507510.1209/0295-5075/100/60004 100, 60004 (2012)]. In this Brief Report, we demonstrate that in perfect translation-invariant systems with an even number of sites, the Bell inequality can be violated. A nontrivial model is constructed to confirm the conclusion.
Information-theoretic temporal Bell inequality and quantum computation
Morikoshi, Fumiaki
2006-05-15
An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality is an immediate consequence of the quantumness in the computation. Furthermore, this approach suggests a notion of temporal nonlocality in quantum computation.
Mathematical and physical meaning of the Bell inequalities
NASA Astrophysics Data System (ADS)
Santos, Emilio
2016-09-01
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values \\{0,1\\}. A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, thus showing a conflict between quantum mechanics and local realism (Bell's theorem). The relations of the Bell inequalities with contextuality, the Kochen–Specker theorem, and quantum entanglement are briefly discussed.
Classical probability model for Bell inequality
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2014-04-01
We show that by taking into account randomness of realization of experimental contexts it is possible to construct common Kolmogorov space for data collected for these contexts, although they can be incompatible. We call such a construction "Kolmogorovization" of contextuality. This construction of common probability space is applied to Bell's inequality. It is well known that its violation is a consequence of collecting statistical data in a few incompatible experiments. In experiments performed in quantum optics contexts are determined by selections of pairs of angles (θi,θ'j) fixing orientations of polarization beam splitters. Opposite to the common opinion, we show that statistical data corresponding to measurements of polarizations of photons in the singlet state, e.g., in the form of correlations, can be described in the classical probabilistic framework. The crucial point is that in constructing the common probability space one has to take into account not only randomness of the source (as Bell did), but also randomness of context-realizations (in particular, realizations of pairs of angles (θi, θ'j)). One may (but need not) say that randomness of "free will" has to be accounted for.
A loophole-free Bell's inequality experiment
NASA Technical Reports Server (NTRS)
Kwiat, Paul G.; Steinberg, Aephraim M.; Chiao, Raymond Y.; Eberhard, Philippe H.
1994-01-01
The proof of Nature's nonlocality through Bell-type experiments is a topic of longstanding interest. Nevertheless, no experiments performed thus far have avoided the so-called 'detection loophole,' arising from low detector efficiencies and angular-correlation difficulties. In fact, most, if not all, of the systems employed to date can never close this loophole, even with perfect detectors. In addition, another loophole involving the non-rapid, non-random switching of various parameter settings exists in all past experiments. We discuss a proposal for a potentially loophole-free Bell's inequality experiment. The source of the EPR-correlated pairs consists of two simultaneously-pumped type-2 phase-matched nonlinear crystals and a polarizing beam splitter. The feasibility of such a scheme with current detector technology seems high, and will be discussed. We also present a single-crystal version, motivated by other work presented at this conference. In a separate experiment, we have measured the absolute detection efficiency and time response of four single-photon detectors. The highest observed efficiencies were 70.7 plus or minus 1.9 percent (at 633 nm, with a device from Rockwell International) and 76.4 plus or minus 2.3 percent (at 702 nm, with an EG&G counting module). Possible efficiencies as high as 90 percent were implied. The EG&G devices displayed sub-nanosecond time resolution.
Higher-dimensional Bell inequalities with noisy qudits
NASA Astrophysics Data System (ADS)
Polozova, Elena; Strauch, Frederick W.
2016-03-01
Generalizations of the classic Bell inequality to higher-dimensional quantum systems known as qudits are reputed to exhibit a higher degree of robustness to noise but such claims are based on one particular noise model. We analyze the violation of the Collins-Gisin-Linden-Massar-Popescu inequality subject to more realistic noise sources and their scaling with dimension. This analysis is inspired by potential Bell inequality experiments with superconducting resonator-based qudits. We find that the robustness of the inequality to noise generally decreases with increasing qudit dimension.
Exclusivity principle and the quantum bound of the Bell inequality
NASA Astrophysics Data System (ADS)
Cabello, Adán
2014-12-01
We show that, for general probabilistic theories admitting sharp measurements, the exclusivity principle together with two assumptions exactly singles out the Tsirelson bound of the Clauser-Horne-Shimony-Holt Bell inequality.
The strong Bell inequalities: A proposed experimental test
NASA Technical Reports Server (NTRS)
Fry, Edward S.
1994-01-01
All previous experimental tests of Bell inequalities have required additional assumptions. The strong Bell inequalities (i.e. those requiring no additional assumptions) have never been tested. An experiment has been designed that can, for the first time, provide a definitive test of the strong Bell inequalities. Not only will the detector efficiency loophole be closed; but the locality condition will also be rigorously enforced. The experiment involves producing two Hg-199 atoms by a resonant Raman dissociation of a mercury dimer ((199)Hg2) that is in an electronic and nuclear spin singlet state. Bell inequalities can be tested by measuring angular momentum correlations between the spin one-half nuclei of the two Hg-199 atoms. The method used to make these latter measurements will be described.
Unbounded Violation of Tripartite Bell Inequalities
NASA Astrophysics Data System (ADS)
Pérez-García, D.; Wolf, M. M.; Palazuelos, C.; Villanueva, I.; Junge, M.
2008-04-01
We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck’s constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized Greenberger-Horne-Zeilinger (GHZ) states is always bounded so that, in contrast to many other contexts, GHZ states do not lead to extremal quantum correlations in this case. In order to derive all these physical consequences, we will have to obtain new mathematical results in the theories of operator spaces and tensor norms. In particular, we will prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras. Finally, we will relate the existence of diagonal states leading to unbounded violations with a long-standing open problem in the context of Banach algebras.
Towards Loophole-Free Optical Bell Test of CHSH Inequality
NASA Astrophysics Data System (ADS)
Tan, Yong-gang; Li, Hong-wei
2016-04-01
Bell test had been suggested to end the long-standing debate on the EPR paradox, while the imperfections of experimental devices induce some loopholes in Bell test experiments and hence the assumption of local reality by EPR cannot be excluded with current experimental results. In optical Bell test experiments, the locality loophole can be closed easily, while the attempt of closing detection loophole requires very high efficiency of single photon detectors. Previous studies showed that the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with maximally entangled states requires the detection efficiency to be higher than 82.8 %. In this paper, we raise a modified CHSH inequality that covers all measurement events including the efficient and inefficient detections in the Bell test and prove that all local hidden models can be excluded when the inequality is violated. We find that, when non-maximally entangled states are applied to the Bell test, the lowest detection efficiency for violation of the present inequality is 66.7 %. This makes it feasible to close the detection loophole and the locality loophole simultaneously in optical Bell test of CHSH inequality.
Towards Loophole-Free Optical Bell Test of CHSH Inequality
NASA Astrophysics Data System (ADS)
Tan, Yong-gang; Li, Hong-wei
2016-09-01
Bell test had been suggested to end the long-standing debate on the EPR paradox, while the imperfections of experimental devices induce some loopholes in Bell test experiments and hence the assumption of local reality by EPR cannot be excluded with current experimental results. In optical Bell test experiments, the locality loophole can be closed easily, while the attempt of closing detection loophole requires very high efficiency of single photon detectors. Previous studies showed that the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with maximally entangled states requires the detection efficiency to be higher than 82.8 %. In this paper, we raise a modified CHSH inequality that covers all measurement events including the efficient and inefficient detections in the Bell test and prove that all local hidden models can be excluded when the inequality is violated. We find that, when non-maximally entangled states are applied to the Bell test, the lowest detection efficiency for violation of the present inequality is 66.7 %. This makes it feasible to close the detection loophole and the locality loophole simultaneously in optical Bell test of CHSH inequality.
Bell Inequalities, Experimental Protocols and Contextuality
NASA Astrophysics Data System (ADS)
Kupczynski, Marian
2015-07-01
In this paper we give additional arguments in favor of the point of view that the violation of Bell, CHSH and CH inequalities is not due to a mysterious non locality of nature. We concentrate on an intimate relation between a protocol of a random experiment and a probabilistic model which is used to describe it. We discuss in a simple way differences between attributive joint probability distributions and generalized joint probability distributions of outcomes from distant experiments which depend on how the pairing of these outcomes is defined. We analyze in detail experimental protocols implied by local realistic and stochastic hidden variable models and show that they are incompatible with the protocols used in spin polarization correlation experiments. We discuss also the meaning of "free will", differences between quantum and classical filters, contextuality of Kolmogorov models, contextuality of quantum theory (QT) and show how this contextuality has to be taken into account in probabilistic models trying to explain in an intuitive way the predictions of QT. The long range imperfect correlations between the clicks of distant detectors can be explained by partially preserved correlations between the signals created by a source. These correlations can only be preserved if the clicks are produced in a local and deterministic way depending on intrinsic parameters describing signals and measuring devices in the moment of the measurement. If an act of a measurement was irreducibly random they would be destroyed. It seems to indicate that QT may be in fact emerging from some underlying more detailed theory of physical phenomena. If this was a case then there is a chance to find in time series of experimental data some fine structures not predicted by QT. This would be a major discovery because it would not only prove that QT does not provide a complete description of individual physical systems but it would prove that it is not predictably complete.
Self-testing protocols based on the chained Bell inequalities
NASA Astrophysics Data System (ADS)
Šupić, I.; Augusiak, R.; Salavrakos, A.; Acín, A.
2016-03-01
Self-testing is a device-independent technique based on non-local correlations whose aim is to certify the effective uniqueness of the quantum state and measurements needed to produce these correlations. It is known that the maximal violation of some Bell inequalities suffices for this purpose. However, most of the existing self-testing protocols for two devices exploit the well-known Clauser–Horne–Shimony–Holt Bell inequality or modifications of it, and always with two measurements per party. Here, we generalize the previous results by demonstrating that one can construct self-testing protocols based on the chained Bell inequalities, defined for two devices implementing an arbitrary number of two-output measurements. On the one hand, this proves that the quantum state and measurements leading to the maximal violation of the chained Bell inequality are unique. On the other hand, in the limit of a large number of measurements, our approach allows one to self-test the entire plane of measurements spanned by the Pauli matrices X and Z. Our results also imply that the chained Bell inequalities can be used to certify two bits of perfect randomness.
Violations of Bell inequalities from random pure states
NASA Astrophysics Data System (ADS)
Atkin, Max R.; Zohren, Stefan
2015-07-01
We consider the expected violations of Bell inequalities from random pure states. More precisely, we focus on a slightly generalized version of the Collins-Gisin-Linden-Massar-Popescu inequality, which concerns Bell experiments of two parties, two measurement options, and N outcomes, and analyze their expected quantum violations from random pure states for varying N , assuming the conjectured optimal measurement operators. It is seen that for small N the Bell inequality is not violated on average, while for larger N it is. Both ensembles of unstructured as well as structured random pure states are considered. Using techniques from random matrix theory this is obtained analytically for small and large N and numerically for intermediate N . The results show a beautiful interplay of different aspects of random matrix theory, ranging from the Marchenko-Pastur distribution and fixed-trace ensembles to the O (n ) model.
Experimental violation of Bell inequalities for multi-dimensional systems.
Lo, Hsin-Pin; Li, Che-Ming; Yabushita, Atsushi; Chen, Yueh-Nan; Luo, Chih-Wei; Kobayashi, Takayoshi
2016-01-01
Quantum correlations between spatially separated parts of a d-dimensional bipartite system (d ≥ 2) have no classical analog. Such correlations, also called entanglements, are not only conceptually important, but also have a profound impact on information science. In theory the violation of Bell inequalities based on local realistic theories for d-dimensional systems provides evidence of quantum nonlocality. Experimental verification is required to confirm whether a quantum system of extremely large dimension can possess this feature, however it has never been performed for large dimension. Here, we report that Bell inequalities are experimentally violated for bipartite quantum systems of dimensionality d = 16 with the usual ensembles of polarization-entangled photon pairs. We also estimate that our entanglement source violates Bell inequalities for extremely high dimensionality of d > 4000. The designed scenario offers a possible new method to investigate the entanglement of multipartite systems of large dimensionality and their application in quantum information processing. PMID:26917246
Violation of Bell inequality based on S4 symmetry
NASA Astrophysics Data System (ADS)
Bolonek-Lasoń, Katarzyna
2016-08-01
In two recent papers [Phys. Rev. A 90, 062121 (2014), 10.1103/PhysRevA.90.062121 and Phys. Rev. A, 91, 052110 (2015), 10.1103/PhysRevA.91.052110] an interesting method of analyzing the violation of Bell inequalities has been proposed which is based on the theory of finite group representations. Here we apply this method to more complicated examples of S4 symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of three-dimensional representations of S4 determined by the geometry of tetrahedron we find that the Bell inequality under consideration is violated in quantum theory. The corresponding nonlocal game is analyzed.
Experimental violation of Bell inequalities for multi-dimensional systems
NASA Astrophysics Data System (ADS)
Lo, Hsin-Pin; Li, Che-Ming; Yabushita, Atsushi; Chen, Yueh-Nan; Luo, Chih-Wei; Kobayashi, Takayoshi
2016-02-01
Quantum correlations between spatially separated parts of a d-dimensional bipartite system (d ≥ 2) have no classical analog. Such correlations, also called entanglements, are not only conceptually important, but also have a profound impact on information science. In theory the violation of Bell inequalities based on local realistic theories for d-dimensional systems provides evidence of quantum nonlocality. Experimental verification is required to confirm whether a quantum system of extremely large dimension can possess this feature, however it has never been performed for large dimension. Here, we report that Bell inequalities are experimentally violated for bipartite quantum systems of dimensionality d = 16 with the usual ensembles of polarization-entangled photon pairs. We also estimate that our entanglement source violates Bell inequalities for extremely high dimensionality of d > 4000. The designed scenario offers a possible new method to investigate the entanglement of multipartite systems of large dimensionality and their application in quantum information processing.
EPR Correlations, Bell Inequalities and Common Cause Systems
NASA Astrophysics Data System (ADS)
Hofer-Szabó, Gábor
2014-03-01
Standard common causal explanations of the EPR situation assume a so-called joint common cause system that is a common cause for all correlations. However, the assumption of a joint common cause system together with some other physically motivated assumptions concerning locality and no-conspiracy results in various Bell inequalities. Since Bell inequalities are violated for appropriate measurement settings, a local, non-conspiratorial joint common causal explanation of the EPR situation is ruled out. But why do we assume that a common causal explanation of a set of correlation consists in finding a joint common cause system for all correlations and not just in finding separate common cause systems for the different correlations? What are the perspectives of a local, non-conspiratorial separate common causal explanation for the EPR scenario? And finally, how do Bell inequalities relate to the weaker assumption of separate common cause systems?
Quantum communication complexity advantage implies violation of a Bell inequality.
Buhrman, Harry; Czekaj, Łukasz; Grudka, Andrzej; Horodecki, Michał; Horodecki, Paweł; Markiewicz, Marcin; Speelman, Florian; Strelchuk, Sergii
2016-03-22
We obtain a general connection between a large quantum advantage in communication complexity and Bell nonlocality. We show that given any protocol offering a sufficiently large quantum advantage in communication complexity, there exists a way of obtaining measurement statistics that violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily large, the ratio of the quantum value to the classical value of the Bell quantity becomes unbounded with the increase in the number of inputs and outputs. PMID:26957600
Quantum communication complexity advantage implies violation of a Bell inequality
NASA Astrophysics Data System (ADS)
Buhrman, Harry; Czekaj, Łukasz; Grudka, Andrzej; Horodecki, Michał; Horodecki, Paweł; Markiewicz, Marcin; Speelman, Florian; Strelchuk, Sergii
2016-03-01
We obtain a general connection between a large quantum advantage in communication complexity and Bell nonlocality. We show that given any protocol offering a sufficiently large quantum advantage in communication complexity, there exists a way of obtaining measurement statistics that violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily large, the ratio of the quantum value to the classical value of the Bell quantity becomes unbounded with the increase in the number of inputs and outputs.
Maximal violation of Bell inequalities by position measurements
Kiukas, J.; Werner, R. F.
2010-07-15
We show that it is possible to find maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality using only position measurements on a pair of entangled nonrelativistic free particles. The device settings required in the CHSH inequality are done by choosing one of two times at which position is measured. For different assignments of the '+' outcome to positions, namely, to an interval, to a half-line, or to a periodic set, we determine violations of the inequalities and states where they are attained. These results have consequences for the hidden variable theories of Bohm and Nelson, in which the two-time correlations between distant particle trajectories have a joint distribution, and hence cannot violate any Bell inequality.
Ito, Tsuyoshi; Imai, Hiroshi; Avis, David
2006-04-15
We show that some two-party Bell inequalities with two-valued observables are stronger than the CHSH inequality for 3x3 isotropic states in the sense that they are violated by some isotropic states in the 3x3 system that do not violate the CHSH inequality. These Bell inequalities are obtained by applying triangular elimination to the list of known facet inequalities of the cut polytope on nine points. This gives a partial solution to an open problem posed by Collins and Gisin. The results of numerical optimization suggest that they are candidates for being stronger than the I{sub 3322} Bell inequality for 3x3 isotropic states. On the other hand, we found no Bell inequalities stronger than the CHSH inequality for 2x2 isotropic states. In addition, we illustrate an inclusion relation among some Bell inequalities derived by triangular elimination.
Multisetting Bell-type inequalities for detecting genuine multipartite entanglement
Pal, Karoly F.; Vertesi, Tamas
2011-06-15
In a recent paper, Bancal et al.[Phys. Rev. Lett. 106, 250404 (2011)] put forward the concept of device-independent witnesses of genuine multipartite entanglement. These witnesses are capable of verifying genuine multipartite entanglement produced in a laboratory without resorting to any knowledge of the dimension of the state space or of the specific form of the measurement operators. As a by-product they found a multiparty three-setting Bell inequality which makes it possible to detect genuine n-partite entanglement in a noisy n-qubit Greenberger-Horne-Zeilinger (GHZ) state for visibilities as low as 2/3 in a device-independent way. In this paper, we generalize this inequality to an arbitrary number of settings, demonstrating a threshold visibility of 2/{pi}{approx}0.6366 for number of settings going to infinity. We also present a pseudotelepathy Bell inequality achieving the same threshold value. We argue that our device-independent witnesses are optimal in the sense that for n odd the above value cannot be beaten with n-party-correlation Bell inequalities.
Violations of multisetting quaternion and octonion Bell inequalities
NASA Astrophysics Data System (ADS)
Kiesewetter, S.; Drummond, P. D.; Reid, M. D.
2015-09-01
We examine the N -partite quaternion and octonion dichotomic Bell inequalities derived by Vogel and Shchukin utilizing the square identities of Euler and Degen, which apply to experiments with M settings at each spatially separated site. We reveal these inequalities to be violated by the Greenberger-Horne-Zeilinger state, for N ≥3 and 2 ≤M ≤8 . Violations are robust with respect to loss, the threshold detection efficiency being η >22/N -1 for all M , implying violations for efficiencies as low as η ˜50 % at each site, as N →∞ .
NASA Astrophysics Data System (ADS)
Das, Siddhartha; Aravinda, S.; Srikanth, R.; Home, Dipankar
2013-12-01
The Bell-type (spatial), Kochen-Specker (contextuality) or Leggett-Garg (temporal) inequalities are based on classically plausible but otherwise quite distinct assumptions. For any of these inequalities, satisfaction is equivalent to a joint probability distribution for all observables in the experiment. This implies a joint distribution for all pairs of observables, and is indifferent to whether or not they commute in the theory. This indifference underpins a unification of the above inequalities into a general framework of correlation inequalities. When the physical scenario is such that the correlated pairs are all compatible, the resulting correlation is nonsignaling, which may be local or multi-particle, corresponding to contextuality or Bell-type inequalities. If the pairs are incompatible, the resulting correlation corresponds to Leggett-Garg (LG) inequalities. That quantum mechanics (QM) violates all these inequalities suggests a close connection between the local, spatial and temporal properties of the theory. As a concrete manifestation of the unification, we extend the method due to Roy and Singh (J. Phys. A, 11 (1978) L167) to derive and study a new class of hybrid spatio-temporal inequalities, where the correlated pairs in the experiment are both compatible or incompatible. The implications for cryptography and monogamy inequalities of the unification are briefly touched upon.
Bell's Inequalities and Methods of Quantifying Measures of Entanglement Correlations
NASA Astrophysics Data System (ADS)
Bracken, Paul
2014-08-01
Bell inequalities provide a specific setting for investigating the physics of entanglement in quantum mechanics. They give a basis for providing an experimental realization of these kinds of quantum phenomena and exhibit some of its more unusual consequences. Some useful ways to look at entanglement quantitatively are presented. It is intended that the presentation and results will provide insights which make effective experimental observation easier.
The various versions of Bell's inequality: an alternative proof
NASA Astrophysics Data System (ADS)
Fakhri, H.; Taqavi, M.
2005-06-01
By considering uncommon factors as spacetime events that influence the spin orientations in the EPRB thought experiment, it is intended to show that one can still introduce the correlation functions. These uncommon factors are positioned inside the common lightcone of two particles. Then, Bell inequalities are proved with the preassumptions of local realism and spin conservation law in the context of a new scenario of hidden variables.
Experimental violation of Bell inequalities for multi-dimensional systems
Lo, Hsin-Pin; Li, Che-Ming; Yabushita, Atsushi; Chen, Yueh-Nan; Luo, Chih-Wei; Kobayashi, Takayoshi
2016-01-01
Quantum correlations between spatially separated parts of a d-dimensional bipartite system (d ≥ 2) have no classical analog. Such correlations, also called entanglements, are not only conceptually important, but also have a profound impact on information science. In theory the violation of Bell inequalities based on local realistic theories for d-dimensional systems provides evidence of quantum nonlocality. Experimental verification is required to confirm whether a quantum system of extremely large dimension can possess this feature, however it has never been performed for large dimension. Here, we report that Bell inequalities are experimentally violated for bipartite quantum systems of dimensionality d = 16 with the usual ensembles of polarization-entangled photon pairs. We also estimate that our entanglement source violates Bell inequalities for extremely high dimensionality of d > 4000. The designed scenario offers a possible new method to investigate the entanglement of multipartite systems of large dimensionality and their application in quantum information processing. PMID:26917246
Violation of Bell's inequality with continuous spatial variables
Abouraddy, Ayman F.; Yarnall, Timothy; Saleh, Bahaa E. A.; Teich, Malvin C.
2007-05-15
The Einstein-Podolsky-Rosen (EPR) argument revealed the paradoxical properties of a two-particle system entangled continuously in the spatial parameter. Yet a direct test of quantum nonlocality exhibited by this state, via a violation of Bell's inequality, has not been forthcoming. In this paper, we identify and construct experimental arrangements comprising simple optical components, without nonlinearities or moving parts, that implement operators in the spatial-parity space of single-photon fields that correspond to the familiar Pauli spin operators. We achieve this by first establishing an isomorphism between the single-mode multiphoton electromagnetic-field space spanned by a Fock-state basis and the single-photon multimode electromagnetic-field space spanned by a spatial-eigenmode basis. We then proceed to construct a Hilbert space with a two-dimensional basis of spatial even-odd parity modes. In particular, we describe an arrangement that implements a rotation in the parity space of each photon of an entangled-photon pair, allowing for a straightforward experimental test of Bell's inequality using the EPR state. Finally, the violation of a Bell inequality is quantified in terms of the physical parameters of the two-photon source.
Proposal to Test Bell's Inequality in Electromechanics
NASA Astrophysics Data System (ADS)
Hofer, Sebastian G.; Lehnert, Konrad W.; Hammerer, Klemens
2016-02-01
Optomechanical and electromechanical systems offer an effective platform to test quantum theory and its predictions at macroscopic scales. To date, all experiments presuppose the validity of quantum mechanics, but could in principle be described by a hypothetical local statistical theory. Here we suggest a Bell test using the electromechanical Einstein-Podolski-Rosen entangled state recently generated by Palomaki et al., Science 342, 710 (2013), which would rule out any local and realistic explanation of the measured data without assuming the validity of quantum mechanics at macroscopic scales. It additionally provides a device-independent way to verify electromechanical entanglement. The parameter regime required for our scheme has been demonstrated or is within reach of current experiments.
Proposal to Test Bell's Inequality in Electromechanics.
Hofer, Sebastian G; Lehnert, Konrad W; Hammerer, Klemens
2016-02-19
Optomechanical and electromechanical systems offer an effective platform to test quantum theory and its predictions at macroscopic scales. To date, all experiments presuppose the validity of quantum mechanics, but could in principle be described by a hypothetical local statistical theory. Here we suggest a Bell test using the electromechanical Einstein-Podolski-Rosen entangled state recently generated by Palomaki et al., Science 342, 710 (2013), which would rule out any local and realistic explanation of the measured data without assuming the validity of quantum mechanics at macroscopic scales. It additionally provides a device-independent way to verify electromechanical entanglement. The parameter regime required for our scheme has been demonstrated or is within reach of current experiments. PMID:26943516
Bound on Bell inequalities by fraction of determinism and reverse triangle inequality
NASA Astrophysics Data System (ADS)
Joshi, P.; Horodecki, K.; Horodecki, M.; Horodecki, P.; Horodecki, R.; Li, Ben; Szarek, S. J.; Szarek, T.
2015-09-01
It is an established fact that entanglement is a resource. Sharing an entangled state leads to nonlocal correlations and to violations of Bell inequalities. Such nonlocal correlations illustrate the advantage of quantum resources over classical resources. In this paper, we quantitatively study Bell inequalities with 2 ×n inputs. As found in Gisin et al. [Int. J. Quantum. Inform. 05, 525 (2007), 10.1142/S021974990700289X], quantum mechanical correlations cannot reach the algebraic bound for such inequalities. Here we uncover the heart of this effect, which we call the fraction of determinism. We show that any quantum statistics with two parties and 2 ×n inputs exhibit a nonzero fraction of determinism, and we supply a quantitative bound for it. We then apply it to provide an explicit universal upper bound for Bell inequalities with 2 ×n inputs. As our main mathematical tool, we introduce and prove a reverse triangle inequality, stating in a quantitative way that if some states are far away from a given state, then their mixture is also. The inequality is crucial in deriving the lower bound for the fraction of determinism, but is also of interest on its own.
Relevant multi-setting tight Bell inequalities for qubits and qutrits
NASA Astrophysics Data System (ADS)
Deng, Dong-Ling; Zhou, Zi-Sui; Chen, Jing-Ling
2009-09-01
In the celebrated paper [D. Collins, N. Gisin, J. Phys. A Math. Gen. 37 (2004) 1775], Collins and Gisin presented for the first time a three-setting Bell inequality (here we call it CG inequality for simplicity) which is relevant to the Clauser-Horne-Shimony-Holt (CHSH) inequality. Inspired by their brilliant ideas, we obtained some multi-setting tight Bell inequalities, which are relevant to the CHSH inequality and the CG inequality. Moreover, we generalized the method in the paper [J.L. Chen, D.L. Deng, Phys. Rev. A 79 (2009) 012115] to construct Bell inequality for qubits to higher dimensional system. Based on the generalized method, we present, for the first time, a three-setting tight Bell inequality for two qutrits, which is maximally violated by nonmaximally entangled states and relevant to the Collins-Gisin-Linden-Massar-Popescu inequality.
Relevant multi-setting tight Bell inequalities for qubits and qutrits
Deng Dongling; Zhou Zisui; Chen Jingling
2009-09-15
In the celebrated paper [D. Collins, N. Gisin, J. Phys. A Math. Gen. 37 (2004) 1775], Collins and Gisin presented for the first time a three-setting Bell inequality (here we call it CG inequality for simplicity) which is relevant to the Clauser-Horne-Shimony-Holt (CHSH) inequality. Inspired by their brilliant ideas, we obtained some multi-setting tight Bell inequalities, which are relevant to the CHSH inequality and the CG inequality. Moreover, we generalized the method in the paper [J.L. Chen, D.L. Deng, Phys. Rev. A 79 (2009) 012115] to construct Bell inequality for qubits to higher dimensional system. Based on the generalized method, we present, for the first time, a three-setting tight Bell inequality for two qutrits, which is maximally violated by nonmaximally entangled states and relevant to the Collins-Gisin-Linden-Massar-Popescu inequality.
Maximal violation of tight Bell inequalities for maximal high-dimensional entanglement
Lee, Seung-Woo; Jaksch, Dieter
2009-07-15
We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even d-dimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for two-mode squeezed states.
Single-qubit tests of Bell-like inequalities
Zela, F. de
2007-10-15
This paper discusses some tests of Bell-like inequalities not requiring entangled states. The proposed tests are based on consecutive measurements on a single qubit. Available hidden-variable models for a single qubit [see, e.g., J. S. Bell, Rev. Mod. Phys. 38, 447 (1966)] reproduce the predictions of quantum mechanics and hence violate the Bell-like inequalities addressed in this paper. It is shown how this fact is connected with the state 'collapse' and with its random nature. Thus, it becomes possible to test truly realistic and deterministic hidden-variable models. In this way, it can be shown that a hidden-variable model should entail at least one of the following features: (i) nonlocality, (ii) contextuality, or (iii) discontinuous measurement-dependent probability functions. The last two features are put to the test with the experiments proposed in this paper. A hidden-variable model that is noncontextual and deterministic would be at variance with some predictions of quantum mechanics. Furthermore, the proposed tests are more likely to be loophole-free, as compared to former ones.
Systematic Construction of Bell-Like Inequalities and Proposal of a New Type of Test
NASA Astrophysics Data System (ADS)
Tanimura, Shogo
2013-09-01
Although it is usually argued that the violation of the Bell inequality is a manifestation of the nonlocality of quantum state, we show that it is a manifestation of the noncommutativity of quantum observables that are defined at the same location. From this point of view we invent a method for systematic construction of generalized Bell inequalities and derive a new inequality that belongs to a different type from the traditional Bell inequality. The new inequality provides a severer and fairer test of quantum mechanics.
Testing Quantum Mechanics and Bell's Inequality with Astronomical Observations
NASA Astrophysics Data System (ADS)
Friedman, Andrew S.; Kaiser, David I.; Gallicchio, Jason; Team 1: University of Vienna, Institute for Quantum Optics and Quantum Information; Team 2: UC San Diego Cosmology Group; Team 3: NASA/JPL/Caltech
2016-06-01
We report on an in progress "Cosmic Bell" experiment that will leverage cosmology to test quantum mechanics and Bell's inequality using astronomical observations. Different iterations of our experiment will send polarization-entangled photons through the open air to detectors ~1-100 kilometers apart, whose settings would be rapidly chosen using real-time telescopic observations of Milky Way stars, and eventually distant, causally disconnected, cosmological sources - such as pairs of quasars or patches of the cosmic microwave background - all while the entangled pair is still in flight. This would, for the first time, attempt to fully close the so-called "setting independence" or "free will" loophole in experimental tests of Bell's inequality, whereby an alternative theory could mimic the quantum predictions if the experimental settings choices shared even a small correlation with unknown, local, causal influences a mere few milliseconds prior to the experiment. A full Cosmic Bell test would push any such influence all the way back to the hot big bang, since the end of any period of inflation, 13.8 billion years ago, an improvement of 20 orders of magnitude compared to the best previous experiments. Redshift z > 3.65 quasars observed at optical wavelengths are the optimal candidate source pairs using present technology. Our experiment is partially funded by the NSF INSPIRE program, in collaboration with MIT, UC San Diego, Harvey Mudd College, NASA/JPL/Caltech, and the University of Vienna. Such an experiment has implications for our understanding of nature at the deepest level. By testing quantum mechanics in a regime never before explored, we would at the very least extend our confidence in quantum theory, while at the same time severely constraining large classes of alternative theories. If the experiment were to uncover discrepancies from the quantum predictions, there could be crucial implications for early-universe cosmology, the security of quantum encryption
Two destructive effects of decoherence on Bell inequality violation
Levkovich-Maslyuk, F. L.
2009-05-15
We consider a system of two spin-(1/2) particles, initially in an entangled Bell state. If one of the particles is interacting with an environment (e.g., a collection of N independent spins), the two-particle system undergoes decoherence. Using a simple model of decoherence, we show that this process has two consequences. First, the maximal amount by which the Clauser-Horne-Shimony-Holt inequality is violated decays to zero. Second, the set of directions of measurement for which the inequality is violated is reduced in the course of decoherence. The volume of that set is bounded above by constx|r|{sup 2}, where r is the decoherence factor. We obtain similar results for the case when each of the two particles is in interaction with a separate environment.
Bell inequality for pairs of particle-number-superselection-rule restricted states
Heaney, Libby; Jaksch, Dieter; Lee, Seung-Woo
2010-10-15
Proposals for Bell-inequality tests on systems restricted by the particle-number-superselection rule often require operations that are difficult to implement in practice. In this article, we derive a Bell inequality, where measurements on pairs of states are used as a method to bypass this superselection rule. In particular, we focus on mode entanglement of an arbitrary number of massive particles and show that our Bell inequality detects the entanglement in an identical pair of states when other inequalities fail. However, as the number of particles in the system increases, the violation of our Bell inequality decreases due to the restriction in the measurement space caused by the superselection rule. This Bell test can be implemented using techniques that are routinely used in current experiments.
Separability of quantum states and the violation of Bell-type inequalities
Loubenets, Elena R.
2004-04-01
In contrast to the widespread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where separable quantum state does not satisfy the original Bell inequality although the latter inequality, in its perfect correlation form, is valid for all joint classical measurements. In a very general setting, we discuss inequalities for joint experiments upon a bipartite quantum system. For any separable quantum state, we derive quantum analogs of the original Bell inequality and specify the conditions sufficient for a separable state to satisfy the original Bell inequality. We introduce the extended Clauser-Horne-Shimony-Holt inequality and prove that, for any separable quantum state, this inequality holds for a variety of linear combinations.
Bell-like inequality for the spin-orbit separability of a laser beam
Borges, C. V. S.; Hor-Meyll, M.; Khoury, A. Z.; Huguenin, J. A. O.
2010-09-15
In analogy with Bell's inequality for two-qubit quantum states, we propose an inequality criterion for the nonseparability of the spin-orbit degrees of freedom of a laser beam. A definition of separable and nonseparable spin-orbit modes is used in consonance with the one presented in Phys. Rev. Lett. 99, 160401 (2007). As the usual Bell's inequality can be violated for entangled two-qubit quantum states, we show both theoretically and experimentally that the proposed spin-orbit inequality criterion can be violated for nonseparable modes. The inequality is discussed in both the classical and quantum domains.
Tight correlation-function Bell inequality for multipartite d -dimensional systems
NASA Astrophysics Data System (ADS)
Chen, Jing-Ling; Deng, Dong-Ling
2009-01-01
We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to multipartite d -dimensional systems. All the Bell inequalities based on this generalization take the same simple form as the CHSH inequality. For small systems, numerical results show that the new inequalities are tight and we believe this is also valid for higher-dimensional systems. Moreover, the new inequalities are relevant to the previous ones and, for bipartite systems, our inequality is equivalent to the Collins-Gisin-Linden-Masser-Popescu inequality.
Strong violations of Bell-type inequalities for path-entangled number states
Wildfeuer, Christoph F.; Dowling, Jonathan P.; Lund, Austin P.
2007-11-15
We show that nonlocal correlation experiments on the two spatially separated modes of a maximally path-entangled number state may be performed. They lead to a violation of a Clauser-Horne Bell inequality for any finite photon number N. We also present an analytical expression for the two-mode Wigner function of a maximally path-entangled number state and investigate a Clauser-Horne-Shimony-Holt Bell inequality for such a state. We test other Bell-type inequalities. Some are violated by a constant amount for any N.
Bell-inequality tests using asymmetric entangled coherent states in asymmetric lossy environments
NASA Astrophysics Data System (ADS)
Park, Chae-Yeun; Jeong, Hyunseok
2015-04-01
We study an asymmetric form of the two-mode entangled coherent state (ECS), where the two local amplitudes have different values, as a tool for testing the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We find that the asymmetric ECSs have obvious advantages over the symmetric form of ECSs in testing the Bell-CHSH inequality. We further study an asymmetric strategy in distributing an ECS over a lossy environment and find that such a scheme can significantly increase violation of the inequality.
Characterizing entanglement of an artificial atom and a cavity cat state with Bell's inequality
NASA Astrophysics Data System (ADS)
Vlastakis, Brian; Petrenko, Andrei; Ofek, Nissim; Sun, Luyan; Leghtas, Zaki; Sliwa, Katrina; Liu, Yehan; Hatridge, Michael; Blumoff, Jacob; Frunzio, Luigi; Mirrahimi, Mazyar; Jiang, Liang; Devoret, M. H.; Schoelkopf, R. J.
2015-11-01
The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement in macroscopically distinguishable systems. The hallmark of entanglement is the detection of strong correlations between systems, most starkly demonstrated by the violation of a Bell inequality. No violation of a Bell inequality has been observed for a system entangled with a superposition of coherent states, known as a cat state. Here we use the Clauser-Horne-Shimony-Holt formulation of a Bell test to characterize entanglement between an artificial atom and a cat state, or a Bell-cat. Using superconducting circuits with high-fidelity measurements and real-time feedback, we detect correlations that surpass the classical maximum of the Bell inequality. We investigate the influence of decoherence with states up to 16 photons in size and characterize the system by introducing joint Wigner tomography. Such techniques demonstrate that information stored in superpositions of coherent states can be extracted efficiently, a crucial requirement for quantum computing with resonators.
Williamson, Mark S.; Son Wonmin; Heaney, Libby
2010-09-15
Recently, it was demonstrated by Son et al., Phys. Rev. Lett. 102, 110404 (2009), that a separable bipartite continuous-variable quantum system can violate the Clauser-Horne-Shimony-Holt (CHSH) inequality via operationally local transformations. Operationally local transformations are parametrized only by local variables; however, in order to allow violation of the CHSH inequality, a maximally entangled ancilla was necessary. The use of the entangled ancilla in this scheme caused the state under test to become dependent on the measurement choice one uses to calculate the CHSH inequality, thus violating one of the assumptions used in deriving a Bell inequality, namely, the free will or statistical independence assumption. The novelty in this scheme however is that the measurement settings can be external free parameters. In this paper, we generalize these operationally local transformations for multipartite Bell inequalities (with dichotomic observables) and provide necessary and sufficient conditions for violation within this scheme. Namely, a violation of a multipartite Bell inequality in this setting is contingent on whether an ancillary system admits any realistic local hidden variable model (i.e., whether the ancilla violates the given Bell inequality). These results indicate that violation of a Bell inequality performed on a system does not necessarily imply that the system is nonlocal. In fact, the system under test may be completely classical. However, nonlocality must have resided somewhere, this may have been in the environment, the physical variables used to manipulate the system or the detectors themselves provided the measurement settings are external free variables.
Violation of Bell's inequality using classical measurements and nonlinear local operations
Stobinska, Magdalena; Jeong, Hyunseok; Ralph, Timothy C.
2007-05-15
We find that Bell's inequality can be significantly violated (up to Tsirelson's bound) with two-mode entangled coherent states using only homodyne measurements. This requires Kerr nonlinear interactions for local operations on the entangled coherent states. Our example is a demonstration of Bell-inequality violations using classical measurements. We conclude that entangled coherent states with coherent amplitudes as small as 0.842 are sufficient to produce such violations.
Bell inequality tests of four-photon six-qubit graph states
Gao Weibo; Yao Xingcan; Xu Ping; Lu He; Lu Chaoyang; Yang Tao; Chen Zengbing; Guehne, Otfried; Cabello, Adan; Pan Jianwei
2010-10-15
We now experimentally demonstrate a Y-shaped graph state with photons' polarization and spatial modes as qubits. Based on this state and a linear-type graph state, we report on the experimental realization of two different Bell inequality tests, which represent higher violation than previous Bell tests.
Maximal non-classicality in multi-setting Bell inequalities
NASA Astrophysics Data System (ADS)
Tavakoli, Armin; Zohren, Stefan; Pawlowski, Marcin
2016-04-01
The discrepancy between maximally entangled states and maximally non-classical quantum correlations is well-known but still not well understood. We aim to investigate the relation between quantum correlations and entanglement in a family of Bell inequalities with N-settings and d outcomes. Using analytical as well as numerical techniques, we derive both maximal quantum violations and violations obtained from maximally entangled states. Furthermore, we study the most non-classical quantum states in terms of their entanglement entropy for large values of d and many measurement settings. Interestingly, we find that the entanglement entropy behaves very differently depending on whether N = 2 or N\\gt 2: when N = 2 the entanglement entropy is a monotone function of d and the most non-classical state is far from maximally entangled, whereas when N\\gt 2 the entanglement entropy is a non-monotone function of d and converges to that of the maximally entangled state in the limit of large d.
Bell inequality with an arbitrary number of settings and its applications
Nagata, Koji; Laskowski, Wieslaw; Paterek, Tomasz
2006-12-15
Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results. Moreover, a necessary and sufficient condition for the violation of this inequality is presented. It turns out that the class of nonseparable states which do not admit local realistic description is extended when compared to the two-setting inequalities. However, supporting the conjecture of Peres, quantum states with positive partial transposes with respect to all subsystems do not violate the inequality. Additionally, we follow a general link between Bell inequalities and communication complexity problems, and present a quantum protocol linked with the inequality, which outperforms the best classical protocol.
Violations of Bell inequalities as lower bounds on the communication cost of nonlocal correlations
Pironio, Stefano
2003-12-01
To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality imposes a lower bound on the average communication needed to produce these correlations. Moreover, for every probability distribution there exists an optimal inequality for which the degree of violation gives the minimal average communication. As an example, to produce using classical resources the correlations that maximally violate the Clauser-Horne-Shimony-Holt inequality, ({radical}2)-1{approx_equal}0.4142 bits of communication are necessary and sufficient. For Bell tests performed on two entangled states of dimension d{>=}3 where each party has the choice between two measurements, our results suggest that more communication is needed to simulate outcomes obtained from certain nonmaximally entangled states than maximally entangled ones.
Testing Quantum Mechanics and Bell's Inequality with Astronomical Observations
NASA Astrophysics Data System (ADS)
Friedman, Andrew S.; Gallicchio, Jason; Kaiser, David I.; Guth, Alan H.
2015-01-01
We propose an experiment which would leverage cosmology to test quantum mechanics using astronomical observations. Our experiment would send entangled photons to detectors over 100 kilometers apart, whose settings would be rapidly chosen using real-time telescopic observations of distant, causally disconnected, cosmic sources - such as pairs of quasars or patches of the Cosmic Microwave Background - all while the entangled pair is still in flight. This would, for the first time, close close the so-called "setting independence" or "free will" loophole in experimental tests of Bell's inequality, whereby an alternative theory could mimic the quantum predictions if the experimental settings choices shared even a small correlation with some local "hidden variables" due to unknown causal influences a mere few milliseconds prior to the experiment. Our "Cosmic Bell" experiment would push any such hidden variable conspiracy all the way back to the hot big bang, since the end of any period of inflation, 13.8 Gyr ago, an improvement of 20 orders of magnitude. We demonstrate the real world feasibility of our experimental setup. While causally disjoint patches of the cosmic microwave background radiation at redshift z ~ 1090 could be used to set the detectors, z > 3.65 quasars observed at optical wavelengths are arguably the optimal candidate source pairs using present technology. Our proposal is supported by some of the world's leading quantum experimentalists, who have begun to collaborate with us to conduct the experiment in the next 2-3 years using some of the instrumentation they have already built and used at two astronomical observatories in the Canary Islands. Such an experiment has implications for our understanding of nature at the deepest level. By testing quantum mechanics in a regime never before explored, we would at the very least extend our confidence in quantum theory, while at the same time severely constraining large classes of alternative theories. If the
Guaranteed violation of a Bell inequality without aligned reference frames or calibrated devices.
Shadbolt, Peter; Vértesi, Tamás; Liang, Yeong-Cherng; Branciard, Cyril; Brunner, Nicolas; O'Brien, Jeremy L
2012-01-01
Bell tests - the experimental demonstration of a Bell inequality violation - are central to understanding the foundations of quantum mechanics, and are a powerful diagnostic tool for the development of quantum technologies. To date, Bell tests have relied on careful calibration of measurement devices and alignment of a shared reference frame between two parties - both technically demanding tasks. We show that neither of these operations are necessary, violating Bell inequalities (i) with certainty using unaligned, but calibrated, measurement devices, and (ii) with near-certainty using uncalibrated and unaligned devices. We demonstrate generic quantum nonlocality with randomly chosen measurements on a singlet state of two photons, implemented using a reconfigurable integrated optical waveguide circuit. The observed results demonstrate the robustness of our schemes to imperfections and statistical noise. This approach is likely to have important applications both in fundamental science and quantum technologies, including device-independent quantum key distribution. PMID:22737404
Guaranteed violation of a Bell inequality without aligned reference frames or calibrated devices
Shadbolt, Peter; Vértesi, Tamás; Liang, Yeong-Cherng; Branciard, Cyril; Brunner, Nicolas; O'Brien, Jeremy L.
2012-01-01
Bell tests — the experimental demonstration of a Bell inequality violation — are central to understanding the foundations of quantum mechanics, and are a powerful diagnostic tool for the development of quantum technologies. To date, Bell tests have relied on careful calibration of measurement devices and alignment of a shared reference frame between two parties — both technically demanding tasks. We show that neither of these operations are necessary, violating Bell inequalities (i) with certainty using unaligned, but calibrated, measurement devices, and (ii) with near-certainty using uncalibrated and unaligned devices. We demonstrate generic quantum nonlocality with randomly chosen measurements on a singlet state of two photons, implemented using a reconfigurable integrated optical waveguide circuit. The observed results demonstrate the robustness of our schemes to imperfections and statistical noise. This approach is likely to have important applications both in fundamental science and quantum technologies, including device-independent quantum key distribution. PMID:22737404
Strong monogamies of no-signaling violations for bipartite correlation bell inequalities.
Ramanathan, Ravishankar; Horodecki, Paweł
2014-11-21
The phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as XOR games, and to free unique games. In many instances of interest, we show that the derived relation provides a significant strengthening over previously known results. Our result connects, for the first time, the property of monogamy with that crucial part of the Bell expression that is necessary for revealing a contradiction with local realistic predictions, thus shifting the paradigm in the field of monogamy of correlations. PMID:25479479
Strong Monogamies of No-Signaling Violations for Bipartite Correlation Bell Inequalities
NASA Astrophysics Data System (ADS)
Ramanathan, Ravishankar; Horodecki, Paweł
2014-11-01
The phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as xor games, and to free unique games. In many instances of interest, we show that the derived relation provides a significant strengthening over previously known results. Our result connects, for the first time, the property of monogamy with that crucial part of the Bell expression that is necessary for revealing a contradiction with local realistic predictions, thus shifting the paradigm in the field of monogamy of correlations.
Chen Zeqian
2004-08-01
Maximally entangled states should maximally violate the Bell inequality. It is proved that all two-qubit states that maximally violate the Bell-Clauser-Horne-Shimony-Holt inequality are exactly Bell states and the states obtained from them by local transformations. The proof is obtained by using the certain algebraic properties that Pauli's matrices satisfy. The argument is extended to the three-qubit system. Since all states obtained by local transformations of a maximally entangled state are equally valid entangled states, we thus give the characterizations of maximally entangled states in both the two-qubit and three-qubit systems in terms of the Bell inequality.
NASA Technical Reports Server (NTRS)
Kiess, Thomas E.; Shih, Yan-Hua; Sergienko, A. V.; Alley, Carroll O.
1994-01-01
We report a new two-photon polarization correlation experiment for realizing the Einstein-Podolsky-Rosen-Bohm (EPRB) state and for testing Bell-type inequalities. We use the pair of orthogonally-polarized light quanta generated in Type 2 parametric down conversion. Using 1 nm interference filters in front of our detectors, we observe from the output of a 0.5mm beta - BaB2O4 (BBO) crystal the EPRB correlations in coincidence counts, and measure an associated Bell inequality violation of 22 standard deviations. The quantum state of the photon pair is a polarization analog of the spin-1/2 singlet state.
Two-qubit Bell inequality for which positive operator-valued measurements are relevant
Vertesi, T.; Bene, E.
2010-12-15
A bipartite Bell inequality is derived which is maximally violated on the two-qubit state space if measurements describable by positive operator valued measure (POVM) elements are allowed, rather than restricting the possible measurements to projective ones. In particular, the presented Bell inequality requires POVMs in order to be maximally violated by a maximally entangled two-qubit state. This answers a question raised by N. Gisin [in Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle: Essays in Honour of Abner Shimony, edited by W. C. Myrvold and J. Christian (Springer, The Netherlands, 2009), pp. 125-138].
Tomographic test of Bell's inequality for a time-delocalized single photon
D'Angelo, Milena; Zavatta, Alessandro; Parigi, Valentina; Bellini, Marco
2006-11-15
Time-domain balanced homodyne detection is performed on two well-separated temporal modes sharing a single photon. The reconstructed density matrix of the two-mode system is used to prove and quantify its entangled nature, while the Wigner function is employed for an innovative tomographic test of Bell's inequality based on the theoretical proposal by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Provided some auxiliary assumptions are made, a clear violation of the Banaszek-Bell inequality is found.
Ghostly action at a distance: A non-technical explanation of the Bell inequality
NASA Astrophysics Data System (ADS)
Alford, Mark G.
2016-06-01
We present a non-mathematical explanation of Bell's inequality. Using the inequality, we show how the results of Einstein-Podolsky-Rosen (EPR) experiments violate the principle of strong locality. This indicates, given some reasonable-sounding assumptions, that some sort of faster-than-light influence is present in nature. We discuss the implications, emphasizing the relationship between EPR and the Principle of Relativity, the distinction between causal influences and signals, and the tension between EPR and determinism.
Asymptotic relation between Bell-inequality violations and entanglement distillability
Kwon, Younghun
2010-11-15
We investigate the asymptotic relation between violations of the Mermin-Belinskii-Klyshko inequality and the entanglement distillability of multipartite entangled states, as the number of parties increases. We in particular consider noisy multiqubit GHZ and so-called Duer states in the Mermin-Belinskii-Klyshko inequality, and show that, in the asymptotic limit of the number of parties, the violation of the inequality implies the distillability in almost all bipartitions.
Characterizing entanglement of an artificial atom and a cavity cat state with Bell's inequality.
Vlastakis, Brian; Petrenko, Andrei; Ofek, Nissim; Sun, Luyan; Leghtas, Zaki; Sliwa, Katrina; Liu, Yehan; Hatridge, Michael; Blumoff, Jacob; Frunzio, Luigi; Mirrahimi, Mazyar; Jiang, Liang; Devoret, M H; Schoelkopf, R J
2015-01-01
The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement in macroscopically distinguishable systems. The hallmark of entanglement is the detection of strong correlations between systems, most starkly demonstrated by the violation of a Bell inequality. No violation of a Bell inequality has been observed for a system entangled with a superposition of coherent states, known as a cat state. Here we use the Clauser-Horne-Shimony-Holt formulation of a Bell test to characterize entanglement between an artificial atom and a cat state, or a Bell-cat. Using superconducting circuits with high-fidelity measurements and real-time feedback, we detect correlations that surpass the classical maximum of the Bell inequality. We investigate the influence of decoherence with states up to 16 photons in size and characterize the system by introducing joint Wigner tomography. Such techniques demonstrate that information stored in superpositions of coherent states can be extracted efficiently, a crucial requirement for quantum computing with resonators. PMID:26611724
Characterizing entanglement of an artificial atom and a cavity cat state with Bell's inequality
Vlastakis, Brian; Petrenko, Andrei; Ofek, Nissim; Sun, Luyan; Leghtas, Zaki; Sliwa, Katrina; Liu, Yehan; Hatridge, Michael; Blumoff, Jacob; Frunzio, Luigi; Mirrahimi, Mazyar; Jiang, Liang; Devoret, M. H.; Schoelkopf, R. J.
2015-01-01
The Schrodinger's cat thought experiment highlights the counterintuitive concept of entanglement in macroscopically distinguishable systems. The hallmark of entanglement is the detection of strong correlations between systems, most starkly demonstrated by the violation of a Bell inequality. No violation of a Bell inequality has been observed for a system entangled with a superposition of coherent states, known as a cat state. Here we use the Clauser–Horne–Shimony–Holt formulation of a Bell test to characterize entanglement between an artificial atom and a cat state, or a Bell-cat. Using superconducting circuits with high-fidelity measurements and real-time feedback, we detect correlations that surpass the classical maximum of the Bell inequality. We investigate the influence of decoherence with states up to 16 photons in size and characterize the system by introducing joint Wigner tomography. Such techniques demonstrate that information stored in superpositions of coherent states can be extracted efficiently, a crucial requirement for quantum computing with resonators. PMID:26611724
Proposal for a motional-state Bell inequality test with ultracold atoms
NASA Astrophysics Data System (ADS)
Lewis-Swan, R. J.; Kheruntsyan, K. V.
2015-05-01
We propose and theoretically simulate an experiment for demonstrating a motional-state Bell inequality violation for pairs of momentum-entangled atoms produced in Bose-Einstein condensate collisions. The proposal is based on realizing an atom-optics analog of the Rarity-Tapster optical scheme: it uses laser-induced Bragg pulses to implement two-particle interferometry on the underlying Bell state for two pairs of atomic scattering modes with equal but opposite momenta. The collision dynamics and the sequence of Bragg pulses are simulated using the stochastic Bogoliubov approach in the positive-P representation. We predict values of the Clauser-Horne-Shimony-Holt (CHSH) parameter up to S ≃2.5 for experimentally realistic parameter regimes, showing a strong violation of the CSHS-Bell inequality bounded classically by S ≤2 .
Augusiak, Remigiusz; Horodecki, Pawel
2006-07-15
It is shown that Smolin four-qubit bound entangled states [J. A. Smolin, Phys. Rev. A 63, 032306 (2001)] can maximally violate the simple two-setting Bell inequality similar to the standard Clauser-Horne-Shimony-Holt (CHSH) inequality. The simplicity of the setting and the robustness of the entanglement make it promising for current experimental technology. On the other hand, the entanglement does not allow for secure key distillation, so neither entanglement nor maximal violation of Bell inequalities implies directly the presence of a quantum secure key. As a result, one concludes that two tasks--reducing of communication complexity and cryptography--are not (even qualitatively) equivalent in a quantum multipartite scenario.
Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies
NASA Astrophysics Data System (ADS)
Wieśniak, Marcin; Dutta, Arijit; Ryu, Junghee
2016-01-01
Greenberger-Horne-Zeilinger (GHZ) states are intuitively known to be the most nonclassical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. In the case of two-dimensional systems, it has been shown that GHZ states lead to an exponentially higher robustness of Bell nonclassicality against the white noise for geometrical inequalities than in the case of Weinfurter-Werner-Wolf-Żukowski-Brukner ones. We introduce geometrical Bell inequalities for collections of arbitrarily many systems of any dimensionality. We show that the violation factor of these inequalities grows exponentially with the number of parties and study their behavior in terms of dimensionality of subsystems and number of local measurements. We also investigate various strategies of assigning mathematical objects to events in the experiment, each leading to different violation ratios.
Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres.
Hensen, B; Bernien, H; Dréau, A E; Reiserer, A; Kalb, N; Blok, M S; Ruitenberg, J; Vermeulen, R F L; Schouten, R N; Abellán, C; Amaya, W; Pruneri, V; Mitchell, M W; Markham, M; Twitchen, D J; Elkouss, D; Wehner, S; Taminiau, T H; Hanson, R
2015-10-29
More than 50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in 'loopholes'. Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification. PMID:26503041
Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres
NASA Astrophysics Data System (ADS)
Hensen, B.; Bernien, H.; Dréau, A. E.; Reiserer, A.; Kalb, N.; Blok, M. S.; Ruitenberg, J.; Vermeulen, R. F. L.; Schouten, R. N.; Abellán, C.; Amaya, W.; Pruneri, V.; Mitchell, M. W.; Markham, M.; Twitchen, D. J.; Elkouss, D.; Wehner, S.; Taminiau, T. H.; Hanson, R.
2015-10-01
More than 50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in `loopholes'. Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 +/- 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S <= 2 and found S = 2.42 +/- 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification.
Experimental investigation of the information entropic Bell inequality
NASA Astrophysics Data System (ADS)
Cao, Lian-Zhen; Zhao, Jia-Qiang; Liu, Xia; Yang, Yang; Li, Ying-De; Wang, Xiao-Qin; Chen, Zeng-Bing; Lu, Huai-Xin
2016-04-01
Inequalities of information entropic play a fundamental role in information theory and have been employed effectively in finding bounds on optimal rates of various information-processing tasks. In this paper, we perform the first experimental demonstration of the information-theoretic spin-1/2 inequality using the high-fidelity entangled state. Furthermore, we study the evolution of information difference of entropy when photons passing through different noisy channels and give the experimental rules of the information difference degradation. Our work provides an new essential tool for quantum information processing and measurement, and offers new insights into the dynamics of quantum correlation in open systems.
Experimental investigation of the information entropic Bell inequality.
Cao, Lian-Zhen; Zhao, Jia-Qiang; Liu, Xia; Yang, Yang; Li, Ying-De; Wang, Xiao-Qin; Chen, Zeng-Bing; Lu, Huai-Xin
2016-01-01
Inequalities of information entropic play a fundamental role in information theory and have been employed effectively in finding bounds on optimal rates of various information-processing tasks. In this paper, we perform the first experimental demonstration of the information-theoretic spin-1/2 inequality using the high-fidelity entangled state. Furthermore, we study the evolution of information difference of entropy when photons passing through different noisy channels and give the experimental rules of the information difference degradation. Our work provides an new essential tool for quantum information processing and measurement, and offers new insights into the dynamics of quantum correlation in open systems. PMID:27034104
Experimental investigation of the information entropic Bell inequality
Cao, Lian-Zhen; Zhao, Jia-Qiang; Liu, Xia; Yang, Yang; Li, Ying-De; Wang, Xiao-Qin; Chen, Zeng-Bing; Lu, Huai-Xin
2016-01-01
Inequalities of information entropic play a fundamental role in information theory and have been employed effectively in finding bounds on optimal rates of various information-processing tasks. In this paper, we perform the first experimental demonstration of the information-theoretic spin-1/2 inequality using the high-fidelity entangled state. Furthermore, we study the evolution of information difference of entropy when photons passing through different noisy channels and give the experimental rules of the information difference degradation. Our work provides an new essential tool for quantum information processing and measurement, and offers new insights into the dynamics of quantum correlation in open systems. PMID:27034104
Intermediate states in quantum cryptography and Bell inequalities
Bechmann-Pasquinucci, H.; Gisin, N.
2003-06-01
Intermediate states are known from intercept/resend eavesdropping in the Bennett-Brassard 1984 (BB84) quantum cryptographic protocol. But they also play fundamental roles in the optimal eavesdropping strategy on the BB84 protocol and in the CHSH (Clauser-Horne-Shimony-Holt) inequality. We generalize the intermediate states to an arbitrary dimension and consider intercept/resend eavesdropping, optimal eavesdropping on the generalized BB84 protocol and present a generalized Clauser-Horne-Shimony-Holt inequality for two entangled qudits based on these states.
Bell's inequality, random sequence, and quantum key distribution
NASA Astrophysics Data System (ADS)
Hwang, Won-Young
2005-05-01
The Ekert 1991 quantum key distribution (QKD) protocol appears to be secure regardless of whatever devices legitimate users adopt for the protocol, as long as the devices give a result that violates Bell’s inequality. However, this is not the case if they ignore nondetection events because Eve can make use of the detection loophole, as Larrson showed [Quantum Inf. Comput. 2, 434 (2002)]. We show that even when legitimate users take into account nondetection events Eve can successfully eavesdrop if the QKD system has been appropriately designed by the manufacturer. A loophole utilized here is that of “free choice” (or “real randomness”). Local QKD devices with a pseudorandom sequence generator installed in them can apparently violate Bell’s inequality.
Bell's inequalities for particles of arbitrary spin in fixed analyzers
Mukamel, Ronen; Howell, John C.
2004-11-01
We propose a new set of observables for experiments on entangled particles of arbitrarily large spin that produce significant Clauser-Horne-Shimony-Holt inequality violations for fixed analyzer settings over a wider range of spins than was previously possible. These observables are better suited for experiments where analyzer orientations must be chosen before the spin of the entangled particles is known, such as experiments using polarization entangled downconverted photons.
Violation of Bell inequalities in larger Hilbert spaces: robustness and challenges
NASA Astrophysics Data System (ADS)
Weiss, Werner; Benenti, Giuliano; Casati, Giulio; Guarneri, Italo; Calarco, Tommaso; Paternostro, Mauro; Montangero, Simone
2016-01-01
We explore the challenges posed by the violation of Bell-like inequalities by d-dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems, naturally arising when exploring the quantum-to-classical transition. We show that, although suitable Bell inequalities can be violated, in principle, for any dimension of given subsystems, it is in practice increasingly challenging to detect such violations, even if the system is prepared in a maximally entangled state. We characterize the effects of random perturbations on the state or on the measurement settings, also quantifying the efforts needed to certify the possible violations in case of complete ignorance on the system state at hand.
Towards loophole-free Bell inequality test with preselected unsymmetrical singlet states of light
NASA Astrophysics Data System (ADS)
Stobińska, Magdalena; Töppel, Falk; Sekatski, Pavel; Buraczewski, Adam
2014-02-01
Can a Bell test with no detection loophole be demonstrated for multiphoton entangled states of light within the current technology? We examine the possibility of a postselection-free Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality test with an unsymmetrical polarization singlet. To that end we employ a preselection procedure which is performed prior to the test. It allows using imperfect (coarse-grained) binary photodetection in the test. We show an example of a preselection scheme which improves violation of the CHSH inequality with the micro-macro polarization singlet produced by the optimal quantum cloning. The preselection is realized by a quantum filter which is believed not to be useful for this purpose.
Device-independent state estimation based on Bell's inequalities
Bardyn, C.-E.; Liew, T. C. H.; Massar, S.; McKague, M.; Scarani, V.
2009-12-15
The only information available about an alleged source of entangled quantum states is the amount S by which the Clauser-Horne-Shimony-Holt inequality is violated: nothing is known about the nature of the system or the measurements that are performed. We discuss how the quality of the source can be assessed in this black-box scenario, as compared to an ideal source that would produce maximally entangled states (more precisely, any state for which S=2sq root(2)). To this end, we present several inequivalent notions of fidelity, each one related to the use one can make of the source after having assessed it, and we derive quantitative bounds for each of them in terms of the violation S. We also derive a lower bound on the entanglement of the source as a function of S only.
NASA Astrophysics Data System (ADS)
Kwon, Hyukjoon; Jeong, Hyunseok
2013-11-01
We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measurements give larger but moderate violations for realistic values of detector efficiency. Experimental realization of our proposal seems feasible in the near future for the implementation of a loophole-free Bell inequality test.
Bell inequalities for continuous-variable systems in generic squeezed states
NASA Astrophysics Data System (ADS)
Martin, Jérôme; Vennin, Vincent
2016-06-01
Bell inequalities for continuous-variable bipartite systems are studied. The inequalities are expressed in terms of pseudo-spin operators, and quantum expectation values are calculated for generic two-mode squeezed states characterized by a squeezing parameter r and a squeezing angle φ . Allowing for generic values of the squeezing angle is especially relevant when φ is not under experimental control, such as in cosmic inflation, where small quantum fluctuations in the early universe are responsible for structures formation. Compared to previous studies restricted to φ =0 and to a fixed orientation of the pseudo-spin operators, allowing for φ ≠0 and optimizing the angular configuration leads to a completely new and rich phenomenology. Two dual schemes of approximation are designed that allow for comprehensive exploration of the squeezing parameter space. In particular, it is found that Bell inequalities can be violated when the squeezing parameter r is large enough, r ≳1.12 , and the squeezing angle φ is small enough, φ ≲0.34 e-r .
Pal, Karoly F.; Vertesi, Tamas
2010-08-15
The I{sub 3322} inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In the case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems; however, there is no such evidence for the I{sub 3322} inequality. In this paper a family of measurement operators and states is given which enables us to attain the maximum quantum value in an infinite-dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite-dimensional quantum systems is not enough to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role in obtaining our results for the I{sub 3322} inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.
Analytic quantification of the singlet nonlocality for the first Bell inequality
NASA Astrophysics Data System (ADS)
Parisio, Fernando
2016-03-01
Recently an alternative way to quantifying the Bell nonlocality has been proposed [E. A. Fonseca and F. Parisio, Phys. Rev. A 92, 030101(R) (2015), 10.1103/PhysRevA.92.030101]. In this work we further develop this concept, the volume of violation, and analytically calculate its value for the spin-singlet state with respect to the settings of the first Bell inequality. These settings correspond to three directions in space, or three arbitrary points on the unit sphere. It is shown that the triples of directions that lead to violations in local causality correspond to 1 /3 of all possible configurations. From the perspective of quantum communication, this means that two distant parties that were able to align their measurements in one direction only (the remaining direction in each site being random) have a probability of about 33.3 % to certify their entanglement.
Experimental violation of bell-like inequalities by electronic shot noise.
Forgues, Jean-Charles; Lupien, Christian; Reulet, Bertrand
2015-04-01
We report measurements of the correlations between electromagnetic field quadratures at two frequencies f1=7 GHz and f1=7.5 GHz of the radiation emitted by a tunnel junction placed at very low temperature and excited at frequency f1+f2. We demonstrate the existence of two-mode squeezing and violation of a Bell-like inequality, thereby proving the existence of entanglement in the quantum shot noise radiated by the tunnel junction. PMID:25884119
Event-by-event simulation of experiments to create entanglement and violate Bell inequalities
NASA Astrophysics Data System (ADS)
Michielsen, K.; De Raedt, H.
2013-10-01
We discuss a discrete-event, particle-based simulation approach which reproduces the statistical distributions of Maxwell's theory and quantum theory by generating detection events one-by-one. This event-based approach gives a unified causeand- effect description of quantum optics experiments such as single-photon Mach-Zehnder interferometer, Wheeler's delayed choice, quantum eraser, double-slit, Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments, and various neutron interferometry experiments. We illustrate the approach by application to single-photon Einstein-Podolsky- Rosen-Bohm experiments and single-neutron interferometry experiments that violate a Bell inequality.
Computing the maximum violation of a Bell inequality is an NP-problem
NASA Astrophysics Data System (ADS)
Batle, J.; Ooi, C. H. Raymond; Abdalla, S.; Bagdasaryan, Armen
2016-06-01
The number of steps required in order to maximize a Bell inequality for arbitrary number of qubits is shown to grow exponentially with the number of parties involved. The proof that the optimization of such correlation measure is an NP-problem based on an operational perspective involving a Turing machine, which follows a general algorithm. The implications for the computability of the so-called nonlocality for any number of qubits is similar to recent results involving entanglement or similar quantum correlation-based measures.
Entanglement and Bell's inequality violation above room temperature in metal carboxylates.
Souza, A M; Soares-Pinto, D O; Sarthour, R S; Oliveira, I S; Reis, Mario S; Brandao, Paula; Moreira Dos Santos, Antonio F
2009-01-01
In the present work we show that a particular family of materials, the metal carboxylates, may have entangled states up to very high temperatures. From magnetic-susceptibility measurements, we have estimated the critical temperature below which entanglement exists in the copper carboxylate {Cu-2(O2CH)(4)}{Cu(O2CH)(2)(2-methylpyridine)(2)}, and we have found this to be above room temperature (T-e similar to 630 K). Furthermore, the results show that the system remains maximally entangled until close to similar to 100 K and the Bell's inequality is violated up to nearly room temperature (similar to 290 K).
Pawlowski, M.
2010-09-15
We show that monogamy of Bell's inequality violations, which is strictly weaker condition than the no-signaling principle is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect the no-signaling principle yet still allow for secure communication. This proves that no signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results concerning the security of existing quantum key distribution protocols.
NASA Astrophysics Data System (ADS)
Ghosh, Sankalpa; Kumar, Rahul
We show that the general quantum state of synthetically spin-orbit coupled ultra cold bosonic atom whose condensate was experimentally created recently (Y.J. Lin et al., Nature, 471, 83, (2011)), shows entanglement between motional degrees of freedom (momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provides a unique opportunity to verify fundamental principle like quantum non-contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such atom-laser system and how that influneces quantities like entanglement entropy, violation of Bell like Inequality etc. We also discuss the implication of our result in testing the quantum non-contextuality and Bell's Inequality vioaltion by macroscopic quantum object like Bose-Einstein Condensate of ultra cold atoms.
Seevinck, Michael; Uffink, Jos
2007-10-15
By introducing a quantitative 'degree of commutativity' in terms of the angle between spin observables we present two tight quantitative trade-off relations in the case of two qubits. First, for entangled states, between the degree of commutativity of local observables and the maximal amount of violation of the Bell inequality: if both local angles increase from zero to {pi}/2 (i.e., the degree of local commutativity decreases), the maximum violation of the Bell inequality increases. Secondly, a converse trade-off relation holds for separable states: if both local angles approach {pi}/2 the maximal value obtainable for the correlations in the Bell inequality decreases and thus the non-violation increases. As expected, the extremes of these relations are found in the case of anticommuting local observables where, respectively, the bounds of 2{radical}(2) and {radical}(2) hold for the expectation value of the Bell operator. The trade-off relations show that noncommmutativity gives 'a more than classical result' for entangled states, whereas 'a less than classical result' is obtained for separable states. The experimental relevance of the trade-off relation for separable states is that it provides an experimental test for two qubit entanglement. Its advantages are twofold: in comparison to violations of Bell inequalities it is a stronger criterion and in comparison to entanglement witnesses it needs to make less strong assumptions about the observables implemented in the experiment.
NASA Astrophysics Data System (ADS)
Hach, Edwin E.; Alsing, Paul M.; Gerry, Christopher C.
2016-04-01
We study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality for entangled SU(1,1) coherent states of the form proposed by Perelomov. Specifically, we examine Bell-CHSH violations by such states in the case in which distant observers Alice and Bob perform local, noncompact, SU(1,1) transformations characterized by hyperbolic angles on each of the subsystems and subsequently measure dichotomic observables, namely SU(1,1) parity operators. We find significant violations over a broad range of hyperbolic angles.
NASA Astrophysics Data System (ADS)
Nikitin, N. V.; Sotnikov, V. P.; Toms, K. S.
2015-10-01
A radically new class of Bell inequalities in Wigner's form was obtained on the basis of Kolmorov's axiomatization of probability theory and the hypothesis of locality. These inequalities take explicitly into account the dependence on time (time-dependent Bell inequalities in Wigner's form). By using these inequalities, one can propose a means for experimentally testing Bohr' complementarity principle in the relativistic region. The inequalities in question open broad possibilities for studying correlations of nonrelativistic and relativistic quantum systems in external fields. The violation of the time-dependent inequalities in quantum mechanics was studied by considering the behavior of a pair of anticorrelated spins in a constant external magnetic field and oscillations of neutral pseudoscalar mesons. The decay of a pseudoscalar particle to a fermion-antifermion pair is considered within quantum field theory. In order to test experimentally the inequalities proposed in the present study, it is not necessary to perform dedicated noninvasive measurements required in the Leggett-Garg approach, for example.
Nikitin, N. V. Sotnikov, V.P.; Toms, K. S.
2015-10-15
A radically new class of Bell inequalities in Wigner’s form was obtained on the basis of Kolmorov’s axiomatization of probability theory and the hypothesis of locality. These inequalities take explicitly into account the dependence on time (time-dependent Bell inequalities in Wigner’s form). By using these inequalities, one can propose a means for experimentally testing Bohr’ complementarity principle in the relativistic region. The inequalities in question open broad possibilities for studying correlations of nonrelativistic and relativistic quantum systems in external fields. The violation of the time-dependent inequalities in quantum mechanics was studied by considering the behavior of a pair of anticorrelated spins in a constant external magnetic field and oscillations of neutral pseudoscalar mesons. The decay of a pseudoscalar particle to a fermion–antifermion pair is considered within quantum field theory. In order to test experimentally the inequalities proposed in the present study, it is not necessary to perform dedicated noninvasive measurements required in the Leggett–Garg approach, for example.
Lo Franco, R.; Compagno, G.; Messina, A.; Napoli, A.
2005-11-15
We consider the entanglement of orthogonal generalized Bernoulli states in two separate single-mode high-Q cavities. The expectation values and the correlations of the electric field in the cavities are obtained. We then define, in each cavity, a dichotomic operator expressible in terms of the field states which can be, in principle, experimentally measured by a probe atom that 'reads' the field. Using the quantum correlations of couples of these operators, we construct a Bell's inequality which is shown to be violated for a wide range of the degree of entanglement and which can be tested in a simple way. Thus the cavity fields directly show quantum nonlocal properties. A scheme is also sketched to generate entangled orthogonal generalized Bernoulli states in the two separate cavities.
Geppert, H.; Denkmayr, T.; Sponar, S.; Lemmel, H.; Hasegawa, Y.
2014-01-01
For precise measurements with polarised neutrons high efficient spin-manipulation is required. We developed several neutron optical elements suitable for a new sophisticated setup, i.e., DC spin-turners and Larmor-accelerators which diminish thermal disturbances and depolarisation considerably. The gain in performance is exploited demonstrating violation of a Bell-like inequality for a spin-path entangled single-neutron state. The obtained value of S=2.365(13), which is much higher than previous measurements by neutron interferometry, is 28σ above the limit of S=2 predicted by contextual hidden variable theories. The new setup is more flexible referring to state preparation and analysis, therefore new, more precise measurements can be carried out. PMID:26089579
Hybrid quantum logic and a test of Bell's inequality using two different atomic isotopes.
Ballance, C J; Schäfer, V M; Home, J P; Szwer, D J; Webster, S C; Allcock, D T C; Linke, N M; Harty, T P; Aude Craik, D P L; Stacey, D N; Steane, A M; Lucas, D M
2015-12-17
Entanglement is one of the most fundamental properties of quantum mechanics, and is the key resource for quantum information processing (QIP). Bipartite entangled states of identical particles have been generated and studied in several experiments, and post-selected or heralded entangled states involving pairs of photons, single photons and single atoms, or different nuclei in the solid state, have also been produced. Here we use a deterministic quantum logic gate to generate a 'hybrid' entangled state of two trapped-ion qubits held in different isotopes of calcium, perform full tomography of the state produced, and make a test of Bell's inequality with non-identical atoms. We use a laser-driven two-qubit gate, whose mechanism is insensitive to the qubits' energy splittings, to produce a maximally entangled state of one (40)Ca(+) qubit and one (43)Ca(+) qubit, held 3.5 micrometres apart in the same ion trap, with 99.8 ± 0.6 per cent fidelity. We test the CHSH (Clauser-Horne-Shimony-Holt) version of Bell's inequality for this novel entangled state and find that it is violated by 15 standard deviations; in this test, we close the detection loophole but not the locality loophole. Mixed-species quantum logic is a powerful technique for the construction of a quantum computer based on trapped ions, as it allows protection of memory qubits while other qubits undergo logic operations or are used as photonic interfaces to other processing units. The entangling gate mechanism used here can also be applied to qubits stored in different atomic elements; this would allow both memory and logic gate errors caused by photon scattering to be reduced below the levels required for fault-tolerant quantum error correction, which is an essential prerequisite for general-purpose quantum computing. PMID:26672554
Einstein-Podolsky-Rosen argument and Bell inequalities for Bose-Einstein spin condensates
Laloee, F.; Mullin, W. J.
2008-02-15
We discuss the properties of two Bose-Einstein condensates in different spin states, represented quantum mechanically by a double Fock state. Individual measurements of the spins of the particles are performed in transverse directions (perpendicular to the spin quantization axis), giving access to the relative phase of the two macroscopically occupied states. Before the first spin measurement, the phase is completely undetermined; after a few measurements, a more and more precise knowledge of its value emerges under the effect of the quantum measurement process. This naturally leads to the usual notion of a quasiclassical phase (Anderson phase) and to an interesting transposition of the Einstein-Podolsky-Rosen argument to macroscopic physical quantities. The purpose of this paper is to discuss this transposition, as well as situations where the notion of a quasiclassical phase is no longer sufficient to account for the quantum results, and where significant violations of Bell-type inequalities are predicted. Quantum mechanically, the problem can be treated exactly: the probability for all sequences of results can be expressed in the form of a double integral, depending on all parameters that define the experiment (number of particles, number and angles of measurements). We discuss the differences between this case and the usual two-spin case. We discuss the effect of the many parameters that the experimenters can adjust for their measurements, starting with a discussion of the effect of the angles of measurement (the 'settings'), and then envisaging various choices of the functions that are used to obtain violation of Bell-Clauser-Horne-Shimony-Holt inequalities. We then discuss how the 'sample bias loophole' (often also called 'efficiency loophole') can be closed in this case, by introducing a preliminary sequence of measurements to localize the particles into 'measurement boxes'. We finally show that the same nonlocal effects can be observed with distinguishable
Spin Correlations of Strongly Interacting Massive Fermion Pairs as a Test of Bell's Inequality
Sakai, H.; Saito, T.; Kuboki, H.; Sasano, M.; Yako, K.; Ikeda, T.; Itoh, K.; Kawabata, T.; Maeda, Y.; Suda, K.; Uesaka, T.; Matsui, N.; Satou, Y.; Rangacharyulu, C.; Sekiguchi, K.; Tamii, A.
2006-10-13
We report the results of the first-time test of the local hidden variable theories (Bell-Clauser-Horne-Shimony-Holt) involving strongly interacting pairs of massive spin 1/2 hadrons from the decay of short-lived ({tau}<10{sup -21}sec) {sup 2}He spin-singlet state, populated in the nuclear reaction {sup 2}H+{sup 1}H{yields}{sup 2}He+n. The novel features of this experiment are (a) the use of an 'event body' detector of nearly 100% efficiency to prepare an unbiased sample and (b) a focal-plane polarimeter of full 2{pi} sr acceptance with a random 'post selection' of the reference axes. The spin-correlation function is deduced to be S{sub exp}({pi}/4)=2.83{+-}0.24{sub stat}{+-}0.07{sub sys}. This result is in agreement with nonlocal quantum mechanical prediction and it violates the Bell-CHSH inequality of vertical bar S vertical bar{<=}2 at a confidence level of 99.3%.
Testing Quantum Mechanics and Bell's Inequality with Cosmological Observations of Quasars
NASA Astrophysics Data System (ADS)
Friedman, Andrew S.; Gallicchio, Jason; Kaiser, David I; Guth, Alan
2014-06-01
We discuss a proposed experiment which would leverage cosmology to test quantum mechanics using astronomical observations. Specifically, we aim to close the "setting independence" or so-called "free will" loophole in experimental tests of Bell's inequality by choosing the detector settings (e.g. polarizer orientations) using real-time observations of causally disconnected cosmic sources, for example sufficiently distant quasar pairs, all while the entangled particles are still in flight. This would help close one of the most important remaining Bell test loopholes whereby an alternative theory could mimic the quantum predictions if the experimental settings choices shared even a small correlation with some local "hidden variables" due to unknown causal influences a mere few milliseconds prior to the experiment. Our "Cosmic Bell" experiment would push any such hidden variable conspiracy all the way back to the hot big bang 13.8 Gyr ago, an improvement of 20 orders of magnitude. The talk will demonstrate the real world feasibility of our experimental setup, with emphasis on the theoretical cosmology constraints needed to choose optimal sources. We thus describe general conditions for pairs of cosmological events with arbitrary redshifts and angular separations to have no shared causal pasts since the hot big bang in flat, dark energy dominated, accelerating Friedman-Lemaitre-Robertson-Walker universes like our own. While causally disjoint patches of the cosmic microwave background radiation at redshift z ~ 1090 could be used to set the detectors, z > 3.65 quasars observed at optical wavelengths are arguably the optimal candidate source pairs using present technology that meet the condition of having no shared causal past since the end of any period of inflation, 13.8 Gyr ago. Results are illustrated for our universe with causal structure animations to help visualize the intersections of past light cones for arbitrary event pairs.
NASA Astrophysics Data System (ADS)
Wood, Christopher J.; Spekkens, Robert W.
2015-03-01
An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit . We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles.
Finite violations of a Bell inequality for high spin: An optical realization
Gerry, Christopher C.; Albert, Jaroslav
2005-10-15
Some years ago Peres [Phys. Rev. A 46, 4413 (1992)] described a gedanken experiment for a pair of spatially spin j particles in a singlet state and showed using with a dichotomic observable (essentially a parity operator) that Bell's theorem in the form of the Clauser-Home-Shimony-Holt (CHSH) inequality is violated by a constant amount (24%) in the limit j{yields}{infinity}. In this paper we present a scheme for an optical realization of a state that is very close to the spin-j singlet state using two traveling-wave modes of the quantized field using a 50:50 beam splitter with an input number state. A near-singlet states comes about because the binomial output state of the beam splitter can be written as a sum in terms of states in the form vertical bar j,m>{sub 1}x vertical bar j,-m>{sub 2}, each state being associated with a Holstein-Primakoff realization of the su(2) spin algebra in terms of the Bose operators of each of the field modes, where j=N/2, N being the number of photons passing through the beam splitter. The binomial state can violate the CHSH inequality to a greater degree than does the singlet state.
NASA Astrophysics Data System (ADS)
Rother, Tom
2016-07-01
In this paper I propose a classical optics experiment that results in a maximum violation of a Bell-like inequality. The first part is concerned with the Bell-like inequality (the so-called CHSH-inequality) itself. Its importance and its maximum violation in Quantum Mechanics (QM) are discussed in detail by employing an abstract probability state concept in a 4-dim. but classical event space. A T-matrix that represents the integral part of a corresponding Green's function as well as a statistical operator that contains a negative quasi-probability can be related to the corresponding quantum mechanical experiment. It is demonstrated that the derivation and usage of the T-matrix and the Green's function is equivalent to what is known from classical scattering theory. It is shown moreover that the negative quasi-probability of the statistical operator may be interpreted as a sink of probabilities related to two single events of the considered 4-dim. event space. A necessary condition for the violation of the CHSH-inequality is derived and discussed afterwards. In the second part of this paper I discuss a modification of the 4-dim. event space considered in the first part. It is shown that a combination of conventional Rayleigh scattering with a Mach-Zehnder setup would be able to put this modification into practice. Thus it becomes possible to achieve a maximum violation of the CHSH-inequality, if formulated in terms of intensities, on a pure classical way. The combination of classical light scattering with correlation experiments such as proposed in this paper may open new ways to study and to use the violation of Bell-like inequalities in modern optics.
Yuan Luqi; Das, Sumanta
2011-06-15
We study the polarization-dependent second-order correlation of a pair of photons emitted in a four-level radiative cascade driven by an external field. It is found that the quantum correlations of the emitted photons, degraded by the energy splitting of the intermediate levels in the radiative cascade, can be efficiently revived by a far-detuned external field. The physics of this revival is linked to an induced Stark shift and the formation of dressed states in the system by the nonresonant external field. Furthermore, we investigated the competition between the effect of the coherent external field and incoherent dephasing of the intermediate levels. We find that the degradation of quantum correlations due to the incoherent dephasing can be contained for small dephasing with the external field. We also studied the nonlocality of the correlations by evaluating the Bell inequality in the linear polarization basis for the radiative cascade. We find that the Bell parameter decreases rapidly with increase in the intermediate-level energy splitting or incoherent dephasing rate to the extent that there is no violation. However, the presence of an external field leads to control over the degrading mechanisms and preservation of nonlocal correlation among the photons. This in turn can induce a violation of Bell's inequality in the radiative cascade for arbitrary intermediate-level splitting and small incoherent dephasing.
Lu Huaixin; Zhao Jiaqiang; Cao Lianzhen; Wang Xiaoqin
2011-10-15
There are different families of inequalities that can be used to characterize the entanglement of multiqubit entangled states by the violation of quantum mechanics prediction versus local realism prediction. In a noisy environment, the violation of different inequalities distinguishes a direct from a noise-free environment. That is, each inequality has a different robustness against noise. We investigate theoretically and experimentally this proposition with the Mermin inequality, Bell inequality, and Svetlichny inequality using three-qubit GHZ states for different levels of noise. Our purpose is to determine which one of the inequalities is more robust against noise and thus more suitable to characterize entanglement of states. Our results show that the Mermin inequality is the most robust against stronger noise and is, thus, more suitable for characterizing the entanglement of three-qubit GHZ states in a noisy environment.
NASA Astrophysics Data System (ADS)
Etesse, Jean; Blandino, Rémi; Kanseri, Bhaskar; Tualle-Brouri, Rosa
2014-05-01
We demonstrate that different kinds of mesoscopic quantum states of light can be efficiently generated from a simple iterative scheme. These states exhibit strong non-classical features, and could be of great interest for many applications such as quantum error-correcting codes or fundamental testings. Based on these states, we further propose a protocol allowing a large loophole-free violation of a Clauser-Horne-Shimony-Holt (CHSH)-type Bell's inequality with significant losses, thus showing that the quantum properties of some of these states can exhibit a remarkable robustness to losses.
Comment on 'Separability of quantum states and the violation of Bell-type inequalities'
Simon, Christoph
2005-02-01
The statement by Loubenets [Phys. Rev. A 69, 042102 (2004)] that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local hidden variables. In a Bell-type setting, the notion of classicality used by Loubenets [Phys. Rev. A 69, 042102 (2004)] corresponds to the assumption of perfect correlations if the same observable is measured on both sides. While it is obvious that most separable states do not satisfy this assumption, this does not constitute 'nonclassical' behavior in any usual sense of the word.
Possibilities of a test of the temporal Bell inequalities using the flux qubit coupled to a dcSQUID
NASA Astrophysics Data System (ADS)
Yeh, Mao-Chuang; Leggett, Anthony
2013-03-01
Although then last few years have seen tests of the temporal Bell inequalities (TBI) on microscopic systems with the use of ``ideal negative result'' (INR) measurements, and on macroscopic systems using weak measurement, to date there have been no tests on macroscopic systems using INR measurements. Moreover, in neither case was the assumption of noninvasiveness explicitly tested in an ancillary experiment. Here we propose a complete INR protocol, including the ancillary experiment, for a test of the TBI on a macroscopic system, namely a flux qubit,with the measuring apparatus a dc SQUID. The general setup mirrors that of Knee et al., with the nuclear spins replaced by the flux qubit and the electron spins by the dc SQUID, and we analyze the relation between the theoretical concept of ``venality'' introduced in ref. and the experimental behavior expected in our ancillary test. On the basis of this analysis we assess the current feasibility of the proposed experiment. Supported by Macarthur supplement grant
Beliefs about Intelligence and the Causes of Economic Inequality: Opinions on "The Bell Curve."
ERIC Educational Resources Information Center
Berk, Eric Vanden; Wodtke, Kenneth
Beliefs about intelligence as a cause of economic inequality and the extent to which educational experience, socioeconomic status, and class-consciousness mediate such beliefs were studied. A purposive sample of 184 advanced Business and Social Science university undergraduates and a sample of urban technical college students responded to a…
Nieuwenhuizen, Th. M.
2009-03-10
It is explained on a physical basis how absence of contextuality allows Bell inequalities to be violated, without bringing an implication on locality or realism. Hereto we connect first to the local realistic theory Stochastic Electrodynamics, and then put the argument more broadly. Thus even if Bell Inequality Violation is demonstrated beyond reasonable doubt, it will have no say on local realism.
Possibilities of a test of the temporal Bell inequalities using a flux qubit coupling to a dcSQUID
NASA Astrophysics Data System (ADS)
Yeh, Mao-Chuang; Leggett, Anthony J.
2014-03-01
Although then last few years have seen tests of the temporal Bell inequalities (TBI) on microscopic systems with the use of ``ideal negative result'' (INR) measurements, and on macroscopic systems using weak measurement, to date there have been no tests on macroscopic systems using INR measurements. Moreover, in neither case was the assumption of noninvasiveness explicitly tested in an ancillary experiment. Here we propose a complete INR protocol, including the ancillary experiment, for a test of the TBI on a macroscopic system, namely a flux qubit,with the measuring apparatus a dc SQUID. The general setup mirrors that of Knee et al., with the nuclear spins replaced by the flux qubit and the electron spins by the dc SQUID, and we analyze the relation between the theoretical concept of ``venality'''' introduced in ref. and the experimental behavior expected in our ancillary test. On the basis of this analysis we assess the current feasibility of the proposed experiment. Supported by the Macarthur Profesorship endowed by the John D. and Catherine T. Macarthur Foundation at the University of Illinois.
Jeong, Hyunseok; Nguyen Ba An
2006-08-15
We study Greenberger-Horne-Zeilinger-type (GHZ-type) and W-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the W-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.
NASA Astrophysics Data System (ADS)
Vallés, Adam; D'Ambrosio, Vincenzo; Hendrych, Martin; Mičuda, Michal; Marrucci, Lorenzo; Sciarrino, Fabio; Torres, Juan P.
2014-11-01
We demonstrate a scheme to generate noncoherent and coherent correlations, i.e., a tunable degree of entanglement, between degrees of freedom of a single photon. Its nature is analogous to the tuning of the purity (first-order coherence) of a single photon forming part of a two-photon state by tailoring the correlations between the paired photons. Therefore, well-known tools such as the Clauser-Horne-Shimony-Holt (CHSH) Bell-like inequality can also be used to characterize entanglement between degrees of freedom. More specifically, CHSH inequality tests are performed, making use of the polarization and the spatial shape of a single photon. The four modes required are two polarization modes and two spatial modes with different orbital angular momentum.
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Anti-Bell - Refutation of Bell's theorem
NASA Astrophysics Data System (ADS)
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
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NASA Astrophysics Data System (ADS)
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
NASA Astrophysics Data System (ADS)
Hespel, Bertrand
Au vu des expériences déjà réalisées, il est permis de penser que la violation de l'inégalité de Bell conformément aux prédictions de la mécanique quantique sera bientôt un fait établi. D'après les lectures qui en ont été le plus souvent données, en raison de la non- localité qu'il met en évidence et de l'incompatibilité qu'il y aurait entre cette propriété et celle de localité postulée par la relativité, ce fait annihilerait inéluctablement l'espoir qui animait le fondateur de la physique moderne et bon nombre de ses successeurs: à moins d'accepter d'abandonner l'exigence d'exactitude, nous devrions définitivement nous résoudre à admettre que nous ne pourrons jamais fournir du monde qu'une image incomplète. L'histoire de la philosophie suggère une toute autre interprétation. Lorsqu'on reconstitue les tentatives oubliées menées par Spinoza, Malebranche et Leibniz, pour bâtir, comme Newton, à la suite de Descartes, un Monde tout à la fois exact et complet, ce fait apparaît plutôt comme la preuve empirique que le monde est tout à la fois local et inséparable-phénoménalement local mais fondamentalement inséparable-et qu'une image adéquate ne pourra donc en être donnée qu'à la condition de reconnaître qu'il ne se réduit pas au contenu de l'espace-temps, c'est-à-dire que ce monde qui est l'objet de la physique n'est pas le tout du monde et qu'il convient de prolonger cette science, désormais quantique et relativiste, par une méta-physique.
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Bell's palsy is the most common cause of facial paralysis. It usually affects just one side of the ... become inflamed. You are most likely to get Bell's palsy if you are pregnant, diabetic or sick with ...
Nagata, Koji
2007-08-15
We show that positivity of every partial transpose of N-partite quantum states implies inequalities on Bell correlations which are stronger than standard Bell inequalities by a factor of 2{sup (N-1)/2}. A violation of the inequality implies that the system is in a bipartite distillable entangled state. It turns out that a family of N-qubit bound entangled states proposed by Duer [Phys. Rev. Lett. 87, 230402 (2001)] violates the inequality for N{>=}4.
NASA Astrophysics Data System (ADS)
Spekkens, Robert
2010-03-01
The Bell-Kochen-Specker theorem demonstrates that the predictions of quantum theory are inconsistent with a noncontextual hidden variable model. Significantly, the notion of noncontextuality to which it appeals is only well-defined for models of quantum theory as opposed to models of an arbitrary physical theory and then only for projective measurements and deterministic models thereof. By contrast, the notion of local causality introduced by Bell is not so restricted in its scope. In this talk, I present an operational definition of noncontextuality that recovers the traditional notion as a special case and allows one to define ``noncontextuality inequalities'' for experimental statistics. I will demonstrate that a particular two-party information-processing task, ``parity-oblivious multiplexing,'' is powered by contextuality in the sense that there is an inequality that bounds its performance in noncontextual models, and I will report on an experimental violation of this inequality in good agreement with the quantum predictions. Joint work with Daniel Buzacott, Tony Keehn, Ben Toner and Geoff Pryde.
Quantum correlations in connected multipartite Bell experiments
NASA Astrophysics Data System (ADS)
Tavakoli, Armin
2016-04-01
Bell experiments measure correlations between outcomes of a number of observers measuring on a shared physical state emitted from a single source. Quantum correlations arising in such Bell experiments have been intensively studied over the last decades. Much less is known about the nature of quantum correlations arising in network structures beyond Bell experiments. Such networks can involve many independent sources emitting states to observers in accordance with the network configuration. Here, we will study classical and quantum correlations in a family of networks which can be regarded as compositions of several independent multipartite Bell experiments connected together through a central node. For such networks we present tight Bell-type inequalities which are satisfied by all classical correlations. We study properties of the violations of our inequalities by probability distributions arising in quantum theory.
Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li
2016-01-01
We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. PMID:26911250
NASA Astrophysics Data System (ADS)
Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li
2016-02-01
We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality.
Steering Bell-diagonal states.
Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li
2016-01-01
We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. PMID:26911250
Vakharia, Kavita; Vakharia, Kalpesh
2016-02-01
Bell's palsy is unilateral, acute onset facial paralysis that is a common condition. One in every 65 people experiences Bell's palsy in the course of their lifetime. The majority of patients afflicted with this idiopathic disorder recover facial function. Initial treatment involves oral corticosteroids, possible antiviral drugs, and protection of the eye from desiccation. A small subset of patients may be left with incomplete recovery, synkinesis, facial contracture, or hemifacial spasm. A combination of medical and surgical treatment options exist to treat the long-term sequelae of Bell's palsy. PMID:26611696
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Bell's palsy is the most common cause of facial paralysis. It usually affects just one side of the face. ... from mild to severe and include Twitching Weakness Paralysis Drooping eyelid or corner of mouth Drooling Dry ...
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Causality, Bell's theorem, and Ontic Definiteness
NASA Astrophysics Data System (ADS)
Henson, Joe
2011-03-01
Bell's theorem shows that the reasonable relativistic causal principle known as ``local causality'' is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the better-known assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of ontic definiteness, that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and realistic viewpoints, are also addressed.
NASA Astrophysics Data System (ADS)
Bellac, Michel Le
2014-11-01
The final form of quantum physics, in the particular case of wave mechanics, was established in the years 1925-1927 by Heisenberg, Schrödinger, Born and others, but the synthesis was the work of Bohr who gave an epistemological interpretation of all the technicalities built up over those years; this interpretation will be examined briefly in Chapter 10. Although Einstein acknowledged the success of quantum mechanics in atomic, molecular and solid state physics, he disagreed deeply with Bohr's interpretation. For many years, he tried to find flaws in the formulation of quantum theory as it had been more or less accepted by a large majority of physicists, but his objections were brushed away by Bohr. However, in an article published in 1935 with Podolsky and Rosen, universally known under the acronym EPR, Einstein thought he had identified a difficulty in the by then standard interpretation. Bohr's obscure, and in part beyond the point, answer showed that Einstein had hit a sensitive target. Nevertheless, until 1964, the so-called Bohr-Einstein debate stayed uniquely on a philosophical level, and it was actually forgotten by most physicists, as the few of them aware of it thought it had no practical implication. In 1964, the Northern Irish physicist John Bell realized that the assumptions contained in the EPR article could be tested experimentally. These assumptions led to inequalities, the Bell inequalities, which were in contradiction with quantum mechanical predictions: as we shall see later on, it is extremely likely that the assumptions of the EPR article are not consistent with experiment, which, on the contrary, vindicates the predictions of quantum physics. In Section 3.2, the origin of Bell's inequalities will be explained with an intuitive example, then they will be compared with the predictions of quantum theory in Section 3.3, and finally their experimental status will be reviewed in Section 3.4. The debate between Bohr and Einstein goes much beyond a
John Bell and the nature of the quantum world
NASA Astrophysics Data System (ADS)
Bertlmann, Reinhold A.
2014-10-01
I present my encounter with John Bell at CERN, our collaboration and joint work in particle physics. I also recall our quantum debates and give my personal view on Bell's fundamental work on quantum theory, in particular, on contextuality and nonlocality of quantum physics. Some mathematical and geometric aspects of entanglement are discussed as influence of Bell's theorem. Finally, I make some historical comments on the experimental side of Bell inequalities. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.
Bell Test experiments explained without entanglement
NASA Astrophysics Data System (ADS)
Boyd, Jeffrey
2011-04-01
by Jeffrey H. Boyd. Jeffreyhboyd@gmail.com. John Bell proposed a test of what was called "local realism." However that is a different view of reality than we hold. Bell incorrectly assumed the validity of wave particle dualism. According to our model waves are independent of particles; wave interference precedes the emission of a particle. This results in two conclusions. First the proposed inequalities that apply to "local realism" in Bell's theorem do not apply to this model. The alleged mathematics of "local realism" is therefore wrong. Second, we can explain the Bell Test experimental results (such as the experiments done at Innsbruck) without any need for entanglement, non-locality, or particle superposition.
Bell Experiment with Classical Optical Fields
NASA Astrophysics Data System (ADS)
Little, Bethany; Qian, Xiao-Feng; Howell, John; Eberly, J. H.
We theoretically and experimentally explore the implications of entanglement in statistically classical optical fields. The description of these fields in terms of polarization and amplitude degrees of freedom can take a non-separable form which employs a mathematical description of entanglement often associated with quantum phenomena. By subjecting these optical fields to a Bell analysis, we examine the role of entanglement in marking the quantum-classical boundary. We report a value of the Bell parameter greater than calB = 2 . 54 , many standard deviations outside the limit calB = 2 established by the Clauser-Horne-Shimony-Holt Bell inequality. This suggests that Bell violation has less to do with quantum theory than previously thought, but everything to do with entanglement. University of Rochester Research Award, NSF PHY-1203931, NSF PHY-1505189, and NSF/INSPIRE PHY-1539859.
Two-player conflicting interest Bayesian games and Bell nonlocality
NASA Astrophysics Data System (ADS)
Situ, Haozhen
2016-01-01
Nonlocality, one of the most remarkable aspects of quantum mechanics, is closely related to Bayesian game theory. Quantum mechanics can offer advantages to some Bayesian games, if the payoff functions are related to Bell inequalities in some way, most of these Bayesian games that have been discussed are common interest games. Recently, the first conflicting interest Bayesian game is proposed in Phys. Rev. Lett. 114, 020401 (2015). In the present paper, we present three new conflicting interest Bayesian games where quantum mechanics offers advantages. The first game is linked with Cereceda inequalities, the second game is linked with a generalized Bell inequality with three possible measurement outcomes, and the third game is linked with a generalized Bell inequality with three possible measurement settings.
NASA Astrophysics Data System (ADS)
Emary, Clive; Lambert, Neill; Nori, Franco
2014-01-01
In contrast to the spatial Bell's inequalities which probe entanglement between spatially separated systems, the Leggett-Garg inequalities test the correlations of a single system measured at different times. Violation of a genuine Leggett-Garg test implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. Quantum mechanics violates the inequalities on both accounts and the original motivation for these inequalities was as a test for quantum coherence in macroscopic systems. The last few years has seen a number of experimental tests and violations of these inequalities in a variety of microscopic systems such as superconducting qubits, nuclear spins, and photons. In this article, we provide an introduction to the Leggett-Garg inequalities and review these latest experimental developments. We discuss important topics such as the significance of the non-invasive measurability assumption, the clumsiness loophole, and the role of weak measurements. Also covered are some recent theoretical proposals for the application of Leggett-Garg inequalities in quantum transport, quantum biology and nano-mechanical systems.
Unbounded Violation of Quantum Steering Inequalities
NASA Astrophysics Data System (ADS)
Marciniak, M.; Rutkowski, A.; Yin, Z.; Horodecki, M.; Horodecki, R.
2015-10-01
We construct steering inequalities that exhibit unbounded violation. The concept was to exploit the relationship between steering violation and the uncertainty relation. To this end, we apply mutually unbiased bases and anticommuting observables, known to exhibit the strongest uncertainty. In both cases, we are able to procure unbounded violations. Our approach is much more constructive and transparent than the operator space theory approach employed to obtain large violation of Bell inequalities. Importantly, using anticommuting observables we are able to obtain a dichotomic steering inequality with unbounded violation. Thus far, there is no analogous result for Bell inequalities. Interestingly, both the dichotomic inequality and one of our inequalities cannot be directly obtained from existing uncertainty relations, which strongly suggest the existence of an unknown kind of uncertainty relation.
Exploring inequality violations by classical hidden variables numerically
Vongehr, Sascha
2013-12-15
There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser–Horne–Shimony–Holt (CHSH) inequality is very robust. However, we argue that with the Einstein–Podolsky–Rosen setup, the CHSH is inferior to the Bell inequality, although and because the latter must assume anti-correlation of entangled photon singlet states. We simulate how often quantum behavior violates both inequalities, depending on the number of photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We present hidden variables that violate the Bell and CHSH inequalities with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. We discuss how to present the quantum correlations to a wide audience and conclude that, when defending against claims of hidden classicality, one should demand numerical simulations and insist on anti-correlation and the full amount of Bell violation. -- Highlights: •The widely assumed superiority of the CHSH fails in the EPR problem. •We simulate Bell type inequalities behavior depending on the number of photons. •The core of Bell’s theorem in the EPR setup is introduced in a simple way understandable to a wide audience. •We present hidden variables that violate both inequalities with 50% probability. •Algorithms have been supplied in form of Mathematica programs.
Entanglement, Bell inequality and all that
Narnhofer, Heide; Thirring, Walter
2012-09-15
We start from the geometrical observation that a finite set of pure states correspond to some points on a sphere and their convex span cannot be the whole set of states. If we call the left over entangled we can pursue this picture from the simplest case of a two dimensional Hilbert space to the usual Alice-and-Bob game of entangled states and then move to bigger systems and finely to quantum field theory where almost everything is entangled. On the way we encounter more or less known old friends up from the shell structure of states to the monogamy of squashed entanglement. We study how entanglement can be concentrated on a small slice and how it depends on the particular factorization of the Hilbert space.
Requirements for a loophole-free photonic Bell test using imperfect setting generators
NASA Astrophysics Data System (ADS)
Kofler, Johannes; Giustina, Marissa; Larsson, Jan-Åke; Mitchell, Morgan W.
2016-03-01
Experimental violations of Bell inequalities are in general vulnerable to so-called loopholes. In this work, we analyze the characteristics of a loophole-free Bell test with photons, closing simultaneously the locality, freedom-of-choice, fair-sampling (i.e., detection), coincidence-time, and memory loopholes. We pay special attention to the effect of excess predictability in the setting choices due to nonideal random-number generators. We discuss necessary adaptations of the Clauser-Horne and Eberhard inequality when using such imperfect devices and—using Hoeffding's inequality and Doob's optional stopping theorem—the statistical analysis in such Bell tests.
Position-momentum Bell nonlocality with entangled photon pairs
NASA Astrophysics Data System (ADS)
Schneeloch, James; Knarr, Samuel H.; Lum, Daniel J.; Howell, John C.
2016-01-01
Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Although Bell nearly showed a violation using the Clauser-Horne-Shimony-Holt (CHSH) inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he does not give a quantitative estimation of the maximum achievable violation for the wave function he considers. In this article, we show how his strategy can be reimagined using the transverse positions and momenta of entangled photon pairs measured at different propagation distances, and we find that the maximum achievable violation for the state he considers is actually very small relative to the upper limit of 2 √{2 } . Although Bell's wave function does not produce a large violation of the CHSH inequality, other states may yet do so.
A Geometrical Approach to Bell's Theorem
NASA Technical Reports Server (NTRS)
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
Clauser-Horne Bell test with imperfect random inputs
NASA Astrophysics Data System (ADS)
Yuan, Xiao; Zhao, Qi; Ma, Xiongfeng
2015-08-01
The Bell test is one of the most important tools in quantum information science. On the one hand, it enables fundamental tests of the basic physics laws of nature, and on the other hand, it can also be applied in a variety of device-independent tasks such as quantum key distribution and random number generation. In practice, loopholes existing in experimental demonstrations of Bell tests may affect the validity of the conclusions. In this work, we focus on the randomness (freewill) loophole and investigate the randomness requirement in a well-known Bell test, the Clauser-Horne test, under various conditions. We explicitly bound the Bell value for all local hidden variable models by optimizing over all classical strategies exploiting the knowledge of the partially random inputs. Our result thus provides input randomness requirements on the Clauser-Horne test under varieties of practical scenarios. The employed analysis technique can also be generalized to other Bell inequalities.
NASA Astrophysics Data System (ADS)
Miyake, Hideki; Grzymkowski, Rafal; Ludacka, Radek; Schram, Malachi
2015-12-01
The Belle II experiment will record a similar quantity of data to LHC experiments and will acquire it at similar rates. This requires considerable computing, storage and network resources to handle not only data created by the experiment but also considerable amounts of simulated data. Consequently Belle II employs a distributed computing system to provide the resources coordinated by the the DIRAC interware. DIRAC is a general software framework that provides a unified interface among heterogeneous computing resources. In addition to the well proven DIRAC software stack, Belle II is developing its own extension called BelleDIRAC. BelleDIRAC provides a transparent user experience for the Belle II analysis framework (basf2) on various environments and gives access to file information managed by LFC and AMGA metadata catalog. By unifying DIRAC and BelleDIRAC functionalities, Belle II plans to operate an automated mass data processing framework named a “production system”. The Belle II production system enables large-scale raw data transfer from experimental site to raw data centers, followed by massive data processing, and smart data delivery to each remote site. The production system is also utilized for simulated data production and data analysis. Although development of the production system is still on-going, recently Belle II has prepared prototype version and evaluated it with a large scale simulated data production. In this presentation we will report the evaluation of the prototype system and future development plans.
Bell Correlated and EPR States in the Framework of Jordan Algebras
NASA Astrophysics Data System (ADS)
Hamhalter, Jan; Sobotíková, Veronika
2016-03-01
We study Bell inequalities and EPR states in the context of Jordan algebras. We show that the set of states violating Bell inequalities across two operator commuting nonmodular Jordan Banach algebras is norm dense in the global state space. It generalizes hitherto known results in quantum field theory in several directions. We propose new Jordan quantity for incommensurable observables in a given state, introduce the concept of EPR state for Jordan structures, and study relationship between EPR states and Bell correlated states. Our analysis shows crucial role of spin factors and Pauli spin matrices for studying noncommutative properties of states and observables.
The Pseudoscience of Psychometry and "The Bell Curve."
ERIC Educational Resources Information Center
Graves, Joseph L., Jr.; Johnson, Amanda
1995-01-01
Argues that Herrnstein and Murray's "The Bell Curve" (1994) merely restates the notion that intelligence can be reduced to a single ordinal measure, i.e., the primary factor for determining group or individual social-class status. Evidence from the biological sciences and quantitative genetics is presented that reveals that social inequality is…
NASA Astrophysics Data System (ADS)
Zohren, Stefan; Gill, Richard D.
2008-03-01
We present a much simplified version of the Collins-Gisin-Linden-Massar-Popescu inequality for the 2×2×d Bell scenario. Numerical maximization of the violation of this inequality over all states and measurements suggests that the optimal state is far from maximally entangled, while the best measurements are the same as conjectured best measurements for the maximally entangled state. For very large values of d the inequality seems to reach its minimal value given by the probability constraints. This gives numerical evidence for a tight quantum Bell inequality (or generalized Csirelson inequality) for the 2×2×∞ scenario.
Exploring inequality violations by classical hidden variables numerically
NASA Astrophysics Data System (ADS)
Vongehr, Sascha
2013-12-01
There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very robust. However, we argue that with the Einstein-Podolsky-Rosen setup, the CHSH is inferior to the Bell inequality, although and because the latter must assume anti-correlation of entangled photon singlet states. We simulate how often quantum behavior violates both inequalities, depending on the number of photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We present hidden variables that violate the Bell and CHSH inequalities with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. We discuss how to present the quantum correlations to a wide audience and conclude that, when defending against claims of hidden classicality, one should demand numerical simulations and insist on anti-correlation and the full amount of Bell violation.
Testing Leggett's Inequality Using Aharonov-Casher Effect
Su, Hong-Yi; Chen, Jing-Ling; Wu, Chunfeng; Deng, Dong-Ling; Oh, C. H.
2013-01-01
Bell's inequality is established based on local realism. The violation of Bell's inequality by quantum mechanics implies either locality or realism or both are untenable. Leggett's inequality is derived based on nonlocal realism. The violation of Leggett's inequality implies that quantum mechanics is neither local realistic nor nonlocal realistic. The incompatibility of nonlocal realism and quantum mechanics has been currently confirmed by photon experiments. In our work, we propose to test Leggett's inequality using the Aharonov-Casher effect. In our scheme, four entangled particles emitted from two sources manifest a two-qubit-typed correlation that may result in the violation of the Leggett inequality, while satisfying the no-signaling condition for spacelike separation. Our scheme is tolerant to some local inaccuracies due to the topological nature of the Aharonov-Casher phase. The experimental implementation of our scheme can be possibly realized by a calcium atomic polarization interferometer experiment. PMID:23966132
Bell correlations in a Bose-Einstein condensate
NASA Astrophysics Data System (ADS)
Schmied, Roman; Bancal, Jean-Daniel; Allard, Baptiste; Fadel, Matteo; Scarani, Valerio; Treutlein, Philipp; Sangouard, Nicolas
2016-04-01
Characterizing many-body systems through the quantum correlations between their constituent particles is a major goal of quantum physics. Although entanglement is routinely observed in many systems, we report here the detection of stronger correlations—Bell correlations—between the spins of about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation witness from a many-particle Bell inequality involving only one- and two-body correlation functions. Our measurement on a spin-squeezed state exceeds the threshold for Bell correlations by 3.8 standard deviations. Our work shows that the strongest possible nonclassical correlations are experimentally accessible in many-body systems and that they can be revealed by collective measurements.
Experimentally testing Bell's theorem based on Hardy's nonlocal ladder proofs
NASA Astrophysics Data System (ADS)
Guo, WeiJie; Fan, DaiHe; Wei, LianFu
2015-02-01
Bell's theorem argues the existence of quantum nonlocality which goes basically against the hidden variable theory (HVT). Many experiments have been done via testing the violations of Bell's inequalities to statistically verify the Bell's theorem. Alternatively, by testing the Hardy's ladder proofs we experimentally demonstrate the deterministic violation of HVT and thus confirm the quantum nonlocality. Our tests are implemented with non-maximal entangled photon pairs generated by spontaneous parametric down conversions (SPDCs). We show that the degree freedom of photon entanglement could be significantly enhanced by using interference filters. As a consequence, the Hardy's ladder proofs could be tested and Bell's theorem is verified robustly. The probability of violating the locality reach to 41.9%, which is close to the expectably ideal value 46.4% for the photon pairs with degree of entanglement ɛ = 0.93. The higher violating probability is possible by further optimizing the experimental parameters.
Bell correlations in a Bose-Einstein condensate.
Schmied, Roman; Bancal, Jean-Daniel; Allard, Baptiste; Fadel, Matteo; Scarani, Valerio; Treutlein, Philipp; Sangouard, Nicolas
2016-04-22
Characterizing many-body systems through the quantum correlations between their constituent particles is a major goal of quantum physics. Although entanglement is routinely observed in many systems, we report here the detection of stronger correlations--Bell correlations--between the spins of about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation witness from a many-particle Bell inequality involving only one- and two-body correlation functions. Our measurement on a spin-squeezed state exceeds the threshold for Bell correlations by 3.8 standard deviations. Our work shows that the strongest possible nonclassical correlations are experimentally accessible in many-body systems and that they can be revealed by collective measurements. PMID:27102479
ERIC Educational Resources Information Center
Wagner, Tom
2010-01-01
The ceremonial copper and iron bells at the Smithsonian's National Museum of African Art were the author's inspiration for an interdisciplinary unit with a focus on the contributions various cultures make toward the richness of a community. The author of this article describes an Edo bell-inspired ceramic project incorporating slab-building…
Trabelsi, Karim
2006-02-11
We report recent results on the properties of the X(3872) produced via the B {yields} KX(3872) decay process in the Belle detector. We compare these properties with the expectations for possible assignments. The discoveries by Belle of other new particles : Y(3940), X(3940) and Z(3931) are briefly reviewed as well as the observation of an isotriplet of excited charmed baryons.
Violation of the Leggett-Garg Inequality in Neutrino Oscillations.
Formaggio, J A; Kaiser, D I; Murskyj, M M; Weiss, T E
2016-07-29
The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested. PMID:27517759
Violation of the Leggett-Garg Inequality in Neutrino Oscillations
NASA Astrophysics Data System (ADS)
Formaggio, J. A.; Kaiser, D. I.; Murskyj, M. M.; Weiss, T. E.
2016-07-01
The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6 σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.
Maximal violation of the Clauser-Horne-Shimony-Holt inequality for two qutrits
Fu, Li-Bin; Zhao, Xian-Geng; Chen, Jing-Ling
2003-08-01
The Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality (in terms of correlation functions) of two qutrits is studied in detail by employing tritter measurements. A uniform formula for the maximum value of this inequality for tritter measurements is obtained. Based on this formula, we show that nonmaximally entangled states violate the BCHSH inequality more strongly than the maximally entangled one. This result is consistent with what was obtained by Acin et al. [Phys. Rev. A 65, 052325 (2002)] using the Bell-Clauser-Horne inequality (in terms of probabilities)
NASA Astrophysics Data System (ADS)
Wei, Zhang; Jiali, Hou; Wenfang, Yang
2013-01-01
A number of versions of the well-known "bell-in-a-bell-jar" demonstration have been discussed in this journal.1-3 The basic idea is that when a sound source is placed inside an air-tight container, the volume of the sound that's heard decreases dramatically when the container is evacuated. This phenomenon is primarily due to the mismatch that is created between the sound transducer and the surrounding medium.4,5 Here we describe a simple small-scale version of this demonstration, one that may be added to the growing list of examples of how a simple syringe may be used as a tool in physics teaching.6-8
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory. PMID:20393558
Bell Could Become the Copernicus of Probability
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2016-07-01
Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell’s inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born’s rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model — the first example of the non-Euclidean model of geometry. This is the “probability model” interpretation of the violation of Bell’s inequality. We also criticize the standard interpretation—an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test.
Postselection-Loophole-Free Bell Test Over an Installed Optical Fiber Network.
Carvacho, Gonzalo; Cariñe, Jaime; Saavedra, Gabriel; Cuevas, Álvaro; Fuenzalida, Jorge; Toledo, Felipe; Figueroa, Miguel; Cabello, Adán; Larsson, Jan-Åke; Mataloni, Paolo; Lima, Gustavo; Xavier, Guilherme B
2015-07-17
Device-independent quantum communication will require a loophole-free violation of Bell inequalities. In typical scenarios where line of sight between the communicating parties is not available, it is convenient to use energy-time entangled photons due to intrinsic robustness while propagating over optical fibers. Here we show an energy-time Clauser-Horne-Shimony-Holt Bell inequality violation with two parties separated by 3.7 km over the deployed optical fiber network belonging to the University of Concepción in Chile. Remarkably, this is the first Bell violation with spatially separated parties that is free of the postselection loophole, which affected all previous in-field long-distance energy-time experiments. Our work takes a further step towards a fiber-based loophole-free Bell test, which is highly desired for secure quantum communication due to the widespread existing telecommunication infrastructure. PMID:26230776
Postselection-Loophole-Free Bell Test Over an Installed Optical Fiber Network
NASA Astrophysics Data System (ADS)
Carvacho, Gonzalo; Cariñe, Jaime; Saavedra, Gabriel; Cuevas, Álvaro; Fuenzalida, Jorge; Toledo, Felipe; Figueroa, Miguel; Cabello, Adán; Larsson, Jan-Åke; Mataloni, Paolo; Lima, Gustavo; Xavier, Guilherme B.
2015-07-01
Device-independent quantum communication will require a loophole-free violation of Bell inequalities. In typical scenarios where line of sight between the communicating parties is not available, it is convenient to use energy-time entangled photons due to intrinsic robustness while propagating over optical fibers. Here we show an energy-time Clauser-Horne-Shimony-Holt Bell inequality violation with two parties separated by 3.7 km over the deployed optical fiber network belonging to the University of Concepción in Chile. Remarkably, this is the first Bell violation with spatially separated parties that is free of the postselection loophole, which affected all previous in-field long-distance energy-time experiments. Our work takes a further step towards a fiber-based loophole-free Bell test, which is highly desired for secure quantum communication due to the widespread existing telecommunication infrastructure.
An additional condition for Bell experiments for accepting local realistic theories
NASA Astrophysics Data System (ADS)
Nagata, Koji; Nakamura, Tadao
2013-12-01
We assume that one source of two uncorrelated spin-carrying particles emits them in a state, which can be described as a spin-1/2 bipartite pure uncorrelated state. We consider a Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) experiment with two-orthogonal-settings. We propose an additional condition for the state to be reproducible by the property of local realistic theories. We use the proposed measurement theory in order to construct the additional condition (Nagata and Nakamura in Int J Theor Phys 49:162, 2010). The condition is that local measurement outcome is . Otherwise, such an experiment does not allow for the existence of local realistic theories even in the situation that all Bell-CHSH inequalities hold. Also we derive new set of Bell inequalities when local measurement outcome is.
Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons.
Giustina, Marissa; Versteegh, Marijn A M; Wengerowsky, Sören; Handsteiner, Johannes; Hochrainer, Armin; Phelan, Kevin; Steinlechner, Fabian; Kofler, Johannes; Larsson, Jan-Åke; Abellán, Carlos; Amaya, Waldimar; Pruneri, Valerio; Mitchell, Morgan W; Beyer, Jörn; Gerrits, Thomas; Lita, Adriana E; Shalm, Lynden K; Nam, Sae Woo; Scheidl, Thomas; Ursin, Rupert; Wittmann, Bernhard; Zeilinger, Anton
2015-12-18
Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74×10^{-31}, corresponding to an 11.5 standard deviation effect. PMID:26722905
NASA Astrophysics Data System (ADS)
Paramati, Manjula; Tirumkudulu, Mahesh S.
2016-03-01
A smooth circular moving liquid sheet is formed by the head-on impingement of two equal laminar water jets. We subject such a liquid sheet to uniform laminar air flow from one side such that the direction of air velocity is perpendicular to the liquid sheet. The pressure of the moving air deforms the liquid sheet giving rise to an open water bell. The water bell is symmetric suggesting that the gas flow around the bell is also symmetric and that the gravitational force is negligible. We have captured the shape of the water bells for varying air flow rates and for varying Weber numbers, and compared the measurements with theoretical predictions obtained from a force balance involving liquid inertia, surface tension, and pressure difference across the sheet. The pressure exerted by the gas phase on the front and the rear surface of the deformed liquid sheet is obtained from known results of flow past flat circular discs. The predicted steady state shapes match well with the measurements at low Weber numbers but differences are observed at high Weber numbers, where the sheet flaps and is no longer smooth. Interestingly, the shape predicted by assuming a constant pressure difference equal to the stagnation pressure over the whole of the front face of the sheet and free stream value over the whole of the rear face yields nearly identical results suggesting that an open water bell is similar to a closed water bell in that, to a good approximation, the pressure on either sides of the water bell is homogeneous.
NASA Astrophysics Data System (ADS)
Luo, Cheng-Li; Liao, Chang-Geng; Chen, Zi-Hong
2010-08-01
We investigate the nonlocality dynamics of two initially entangled macroscopic fields each interacting with a resonant two-level atom. The nonlocality of macroscopic field is characterized by the extent to which the Bell Clauser-Horne-Shimony-Holt (CHSH)'s inequality for continuous-variable states is violated. We show that the collapse and revival of the Bell-nonlocality are similar to the collapse and revival of the atomic population inversion of the Jaynes-Cummings model (JCM).
Loophole-free Bell test with one atom and less than one photon on average
Sangouard, N.; Bancal, J.-D.; Gisin, N.; Sekatski, P.; Rosenfeld, W.; Weber, M.; Weinfurter, H.
2011-11-15
We consider the entanglement between two internal states of a single atom and two photon number states describing either the vacuum or a single photon and thus containing, on average, less than one photon. We show that this intriguing entanglement can be characterized through substantial violations of a Bell inequality by performing homodyne detections on the optical mode. We present the experimental challenges that need to be overcome to pave the way toward a loophole-free Bell test.
Revealing Bell's nonlocality for unstable systems in high energy physics
NASA Astrophysics Data System (ADS)
Hiesmayr, Beatrix C.; Di Domenico, Antonio; Curceanu, Catalina; Gabriel, Andreas; Huber, Marcus; Larsson, Jan-Åke; Moskal, Pawel
2012-01-01
Entanglement and its consequences—in particular the violation of Bell inequalities, which defies our concepts of realism and locality—have been proven to play key roles in Nature by many experiments for various quantum systems. Entanglement can also be found in systems not consisting of ordinary matter and light, i.e. in massive meson-antimeson systems. Bell inequalities have been discussed for these systems, but up to date no direct experimental test to conclusively exclude local realism was found. This mainly stems from the fact that one only has access to a restricted class of observables and that these systems are also decaying. In this Letter we put forward a Bell inequality for unstable systems which can be tested at accelerator facilities with current technology. Herewith, the long awaited proof that such systems at different energy scales can reveal the sophisticated " dynamical" nonlocal feature of Nature in a direct experiment gets feasible. Moreover, the role of entanglement and mathcal{CP} violation, an asymmetry between matter and antimatter, is explored, a special feature offered only by these meson-antimeson systems.
Solomon, A. I.
2010-03-15
The 'Bell' of the title refers to bipartite Bell states, and their extensions to, for example, tripartite systems. The 'Group' of the title is the Braid Group in its various representations; while 'Tangle' refers to the property of entanglement which is present in both of these scenarios. The objective of this note is to explore the relation between Quantum Entanglement and Topological Links, and to show that the use of the language of entanglement in both cases is more than one of linguistic analogy.
Software Development at Belle II
NASA Astrophysics Data System (ADS)
Kuhr, Thomas; Hauth, Thomas
2015-12-01
Belle II is a next generation B-factory experiment that will collect 50 times more data than its predecessor Belle. This requires not only a major upgrade of the detector hardware, but also of the simulation, reconstruction, and analysis software. The challenges of the software development at Belle II and the tools and procedures to address them are reviewed in this article.
Hu, Ming-Liang
2012-09-15
Dynamics of disentanglement as measured by the tripartite negativity and Bell nonlocality as measured by the extent of violation of the multipartite Bell-type inequalities are investigated in this work. It is shown definitively that for the initial three-qubit Greenberger-Horne-Zeilinger (GHZ) or W class state preparation, the Bell nonlocality suffers sudden death under the influence of thermal reservoirs. Moreover, all the Bell-nonlocal states are useful for nonclassical teleportation, while there are entangled states that do not violate any Bell-type inequalities, but still yield nonclassical teleportation fidelity. - Highlights: Black-Right-Pointing-Pointer Comparison of different aspects of quantum correlations. Black-Right-Pointing-Pointer Robustness of the initial tripartite GHZ and W class states against decoherence. Black-Right-Pointing-Pointer Bell-nonlocality sudden death under the influence of thermal reservoir. Black-Right-Pointing-Pointer A nonzero minimum tripartite negativity is needed for nonclassical teleportation. Black-Right-Pointing-Pointer All the Bell-nonlocal states yield nonclassical teleportation fidelity.
NASA Technical Reports Server (NTRS)
1943-01-01
Bell XP-77 (Mockup): A proposed lightweight fighter built of non-strategic material (wood) for the Army Air Force, the XP-77 was tested in the 30 x 60 Full Scale Wind Tunnel. This diminutive aircraft never saw production, its physical manifestation limited to two production prototypes which flew in January 1944.
NASA Technical Reports Server (NTRS)
1943-01-01
Bell XP-39 Airacobra: The Army's XP-39 Airacobra in flight over Langley Field, 1943. The pilot of the cobra sat on the front end of the gearbox with the engine behind him and the propeller shaft passing underneath his legs. The P-39 was one of the first military airplanes with tricycle landing gear.
ERIC Educational Resources Information Center
Hamilton, Kendra
2009-01-01
The "Bennett Belle." The words conjure an image that is genteel, old-fashioned--hats and gloves, brown-skinned women in flowing white dresses beaming as they take that final walk to graduation. The Bennett College for Women campus certainly reinforces the image, with its broad, tree-shaded lawns and quadrangle and its historic buildings--fully 15…
Leggett-Garg inequalities and the geometry of the cut polytope
Avis, David; Hayden, Patrick; Wilde, Mark M.
2010-09-15
The Bell and Leggett-Garg tests offer operational ways to demonstrate that nonclassical behavior manifests itself in quantum systems, and experimentalists have implemented these protocols to show that classical worldviews such as local realism and macrorealism are false, respectively. Previous theoretical research has exposed important connections between more general Bell inequalities and polyhedral combinatorics. We show here that general Leggett-Garg inequalities are closely related to the cut polytope of the complete graph, a geometric object well-studied in combinatorics. Building on that connection, we offer a family of Leggett-Garg inequalities that are not trivial combinations of the most basic Leggett-Garg inequalities. We then show that violations of macrorealism can occur in surprising ways, by giving an example of a quantum system that violates the 'pentagon' Leggett-Garg inequality but does not violate any of the basic 'triangle' Leggett-Garg inequalities.
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2016-07-01
The study of socioeconomic inequality is of substantial importance, scientific and general alike. The graphic visualization of inequality is commonly conveyed by Lorenz curves. While Lorenz curves are a highly effective statistical tool for quantifying the distribution of wealth in human societies, they are less effective a tool for the visual depiction of socioeconomic inequality. This paper introduces an alternative to Lorenz curves-the hill curves. On the one hand, the hill curves are a potent scientific tool: they provide detailed scans of the rich-poor gaps in human societies under consideration, and are capable of accommodating infinitely many degrees of freedom. On the other hand, the hill curves are a powerful infographic tool: they visualize inequality in a most vivid and tangible way, with no quantitative skills that are required in order to grasp the visualization. The application of hill curves extends far beyond socioeconomic inequality. Indeed, the hill curves are highly effective 'hyperspectral' measures of statistical variability that are applicable in the context of size distributions at large. This paper establishes the notion of hill curves, analyzes them, and describes their application in the context of general size distributions.
Detection efficiency for loophole-free Bell tests with entangled states affected by colored noise
NASA Astrophysics Data System (ADS)
Cañas, Gustavo; Barra, Johanna F.; Gómez, Esteban S.; Lima, Gustavo; Sciarrino, Fabio; Cabello, Adán
2013-01-01
Loophole-free Bell tests for quantum nonlocality and long-distance secure communication require photodetection efficiencies beyond a threshold ηcrit that depends on the Bell inequality and the noise affecting the entangled state received by the distant parties. Most calculations of ηcrit assume that the noise is random and can be modeled as white noise. However, most sources suffer from colored noise. Indeed, since entangled states are usually created as a superposition of two possible deexcitation paths, a partial distinguishability between the two processes leads to the appearance of colored noise in the generated state. Recently, there was a proposal for a loophole-free Bell test [A. Cabello and F. Sciarrino, Phys. Rev. X 2, 021010 (2012)], where a specific colored noise appears as a consequence of the precertification of the photon's presence through single-photon spontaneous parametric down-conversion. Here we obtain ηcrit, the optimal quantum states, and the local settings for a loophole-free Bell test as a function of the amount of colored noise. We consider three bipartite Bell inequalities with n dichotomic settings: Clauser-Horne-Shimony-Holt (n=2), I3322 (n=3), and A5 (n=4), both for the case of symmetric efficiencies, corresponding to photon-photon Bell tests, and for the totally asymmetric case, corresponding to atom-photon Bell tests. Remarkably, in all these cases, ηcrit is robust against the colored noise. The present analysis can find application in any test of Bell inequalities in which the dominant noise is of the colored type.
NASA Technical Reports Server (NTRS)
1943-01-01
Bell XP-39 Airacobra: The Army's XP-39 Airacobra in flight over Langley Field, 1943. The pilot of the cobra sat on the front end of the gearbox with the engine behind him and the propeller shaft passing underneath his legs. The P-39 was one of the first military airplanes with tricycle landing gear. Photograph published in Engineer in Charge: A History of the Langley Aeronautical Laboratory, 1917-1958 by James R. Hansen. Page 200.
Alexander Graham Bell: Teacher of the Deaf.
ERIC Educational Resources Information Center
Bruce, Robert V.
The lecture on Alexander Graham Bell by Dr. Robert V. Bruce, the author of a biography of Bell, focuses on Bell's association with the Clarke School for the Deaf in Massachusetts. Noted are Bell's employment by the school at 25 years of age and the preceding period during which Bell taught elocution at a boys' school in Scotland and used his…
Ashhab, S.; Nori, Franco; Maruyama, Koji; Brukner, Caslav
2009-12-15
Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intrapair and interpair entanglement. The pairs are taken from a large many-body system where all the pairs are generally entangled with each other. Using an explicit example based on single mode entanglement and an ancillary Bose-Einstein condensate, we show that the Bell-inequality violation in such systems can display statistical properties that are remarkably different from those obtained using identically prepared independent pairs. In particular, one can have probabilistic violation of Bell's inequalities in which a finite fraction of all the runs result in violation even though there could be no violation when averaging over all the runs. Whether or not a particular run of results will end up being local realistically explainable is 'decided' by a sequence of quantum (random) outcomes.
NASA Astrophysics Data System (ADS)
Rossing, Thomas D.
2001-05-01
The art of casting bronze bells developed to a high level of sophistication in China during the Shang dynasty (1766-1123 BC). Many chimes of two-tone bells remain from the Western and Eastern Zhou dynasties (1122-249 BC). With the spread of Buddhism from the third century, large round temple bells developed in China and later in Korea, Japan, and other Asian countries. Vibrational modes of some of these bells have been studied by means of holographic interferometry and experimental modal testing. Their musical as well as acoustical properties are discussed.
NASA Astrophysics Data System (ADS)
Sobie, R. J.
2015-12-01
This paper describes the use of cloud computing resources for the Belle II experiment. A number of different methods are used to exploit the private and opportunistic clouds. Clouds are making significant contributions to the generation of Belle II MC data samples and it is expected that their impact will continue to grow over the coming years.
ERIC Educational Resources Information Center
Breunig, H. Latham
1990-01-01
This article describes the family of Alexander Graham Bell, including research and therapeutic work in speech and hearing impairments spanning three generations. Bell's life and discoveries are discussed, including the formation of the American Association for the Promotion of Teaching of Speech to the Deaf, whose history and organization are…
Bell Test for the Free Motion of Material Particles
Gneiting, Clemens; Hornberger, Klaus
2008-12-31
We present a scheme to establish nonclassical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counterpropagating atoms that is capable of violating a Bell inequality by means of correlated single-particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs Bose-Einstein condensation of fermionic lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology.
Bell test for the free motion of material particles.
Gneiting, Clemens; Hornberger, Klaus
2008-12-31
We present a scheme to establish nonclassical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counterpropagating atoms that is capable of violating a Bell inequality by means of correlated single-particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs Bose-Einstein condensation of fermionic lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology. PMID:19113762
Challenging preconceptions about Bell tests with photon pairs
NASA Astrophysics Data System (ADS)
Caprara Vivoli, V.; Sekatski, P.; Bancal, J.-D.; Lim, C. C. W.; Christensen, B. G.; Martin, A.; Thew, R. T.; Zbinden, H.; Gisin, N.; Sangouard, N.
2015-01-01
Motivated by very recent experiments, we consider a scenario "à la Bell" in which two protagonists test the Clauser-Horne-Shimony-Holt (CHSH) inequality using a photon-pair source based on spontaneous parametric down conversion and imperfect photon detectors. The conventional wisdom says that (i) if the detectors have unit efficiency, the CHSH violation can reach its maximum quantum value of 2 √{2 } . To obtain the maximal possible violation, it suffices that the source emits (ii) maximally entangled photon pairs (iii) in two well-defined single modes. Through a nonperturabive calculation of nonlocal correlations, we show that none of these statements are true. By providing the optimal pump parameters, measurement settings and state structure for any detection efficiency and dark count probability, our results give the recipe to close all the loopholes in a Bell test using photon pairs.
Analysis of a proposal for a realistic loophole-free Bell test with atom-light entanglement
NASA Astrophysics Data System (ADS)
Teo, C.; Minář, J.; Cavalcanti, D.; Scarani, V.
2013-11-01
The violation of Bell inequalities where both detection and locality loopholes are closed is crucial for device-independent assessments of quantum information. While of a technological nature, the simultaneous closing of both loopholes still remains a challenge. In Teo [Nat. Commun.2041-172310.1038/ncomms3104 4, 2104 (2013)], a realistic setup to produce an atom-photon entangled state that could reach a loophole-free Bell inequality violation within current experimental technology is proposed. Here we improve the analysis of this proposal by giving an analytical treatment that shows that the state proposed in Teo [Nat. Commun.2041-172310.1038/ncomms3104 4, 2104 (2013)] can violate a Bell inequality for arbitrarily low photodectection efficiency, when all other losses are ignored. Moreover, it is also able to violate a Bell inequality considering only atomic and homodyne measurements eliminating the need to consider inefficient photocounting measurements. In this case, the maximum Clauser-Horne-Shimony-Holt inequality violation achievable is 2.29, and the minimum transmission required for violation is about 68%. Finally, we show that by postselecting on an atomic measurement, one can engineer superpositions of coherent states for various coherent state amplitudes.
Demonstrating entanglement by testing Bell's theorem in Majorana wires
NASA Astrophysics Data System (ADS)
Drummond, David E.; Kovalev, Alexey A.; Hou, Chang-Yu; Shtengel, Kirill; Pryadko, Leonid P.
2014-09-01
We propose an experiment that would establish the entanglement of Majorana zero modes in semiconductor nanowires by testing the Bell and Clauser-Horne-Shimony-Holt inequalities. Our proposal is viable with realistic system parameters, simple "keyboard" gating, and projective measurement. Theoretical models and simulation results indicate entanglement can be demonstrated with moderately accurate gate operations. In addition to providing further evidence for the existence of the Majorana bound states, our proposal could be used as an experimental stepping stone to more complicated braiding experiments.
Analog of the Clauser-Horne-Shimony-Holt inequality for steering
NASA Astrophysics Data System (ADS)
Cavalcanti, Eric G.; Foster, Christopher J.; Fuwa, Maria; Wiseman, Howard M.
2015-04-01
The Clauser-Horne-Shimony-Holt (CHSH) inequality (and its permutations), are necessary and sufficient criteria for Bell nonlocality in the simplest Bell-nonlocality scenario: 2 parties, 2 measurements per party and 2 outcomes per measurement. Here we derive an inequality for EPR-steering that is an analogue of the CHSH, in that it is necessary and sufficient in this same scenario. However, since in the case of steering the device at Bob's site must be specified (as opposed to the Bell case in which it is a black box), the scenario we consider is that where Alice performs two (black-box) dichotomic measurements, and Bob performs two mutually unbiased qubit measurements. We show that this inequality is strictly weaker than the CHSH, as expected, and use it to decide whether a recent experiment [Phys. Rev. Lett. 110, 130401 (2013).] involving a single-photon split between two parties has demonstrated EPR-steering.
Distributed Computing at Belle II
NASA Astrophysics Data System (ADS)
Bansal, Vikas; Belle Collaboration, II
2016-03-01
The Belle II experiment at the SuperKEKB collider in Tsukuba, Japan, will start physics data taking in 2018 and will accumulate 50 ab-1 of e+e- collision data, about 50 times larger than the data set of the earlier Belle experiment. The computing requirements of Belle II are comparable to those of a RUN I high-pT LHC experiment. Computing will make full use of high speed networking and of the Computing Grids in North America, Asia and Europe. Results of an initial MC simulation campaign with 5 ab-1 equivalent luminosity will be described.
The Trieste Lecture of John Stewart Bell
NASA Astrophysics Data System (ADS)
Bassi, Angelo; Carlo Ghirardi, Gian
2007-03-01
included a picture (figure 1) shown by him, taking it from the tape image which is of rather poor quality (we apologize for this) and three figures taken from his transparencies. Moreover, to help the reader in grasping the various points John Stewart Bell brilliantly raised in his talk we have divided the paper into six sections whose titles have been chosen by us to summarize the most crucial points of his argument. Presentation by the Chairman, Alain Aspect It is a great pleasure and an honour to introduce Professor Bell. When looking to my old papers I discovered that this 25th anniversary of the ICTP also coincides with the famous paper in which appeared, for the first time, inequalities that are now known as Bell's inequalities so it's a very good opportunity to have a talk by John Bell here. Many of us have been strongly influenced by this work of John Bell because he has shown us that quantum mechanics is much more difficult to understand that we thought it was. I am sure that today he will again raise some questions which are very embarrassing but that we have definitely to face.
Nonlocality without inequalities for almost all entangled states of any quantum system
Ghirardi, GianCarlo; Marinatto, Luca
2005-07-15
It is shown that it is possible to rule out all local and stochastic hidden variable models accounting for the quantum mechanical predictions implied by almost any entangled quantum state vector of any number of particles whose Hilbert spaces have arbitrary dimensions, without resorting to Bell-type inequalities. The present proof makes use of the mathematically precise notion of Bell locality and it involves only simple set theoretic arguments.
Effects of reduced measurement independence on Bell-based randomness expansion.
Koh, Dax Enshan; Hall, Michael J W; Setiawan; Pope, James E; Marletto, Chiara; Kay, Alastair; Scarani, Valerio; Ekert, Artur
2012-10-19
With the advent of quantum information, the violation of a Bell inequality is used to witness the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of Bell's theorem is the existence of experimental "free will," meaning that measurement settings can be chosen at random and independently by each party. The relaxation of this assumption potentially shifts the balance of power towards an eavesdropper. We consider a no-signaling model with reduced "free will" and bound the adversary’s capabilities in the task of randomness expansion. PMID:23350071
Bertlmann, Reinhold A.
2015-07-15
John Bell, with whom I had a fruitful collaboration and warm friendship, is best known for his seminal work on the foundations of quantum physics, but he also made outstanding contributions to particle physics and accelerator physics.
Quantum Griffiths Inequalities
NASA Astrophysics Data System (ADS)
Miyao, Tadahiro
2016-07-01
We present a general framework of Griffiths inequalities for quantum systems. Our approach is based on operator inequalities associated with self-dual cones and provides a consistent viewpoint of the Griffiths inequality. As examples, we discuss the quantum Ising model, quantum rotor model, Bose-Hubbard model, and Hubbard model. We present a model-independent structure that governs the correlation inequalities.
Quantum Griffiths Inequalities
NASA Astrophysics Data System (ADS)
Miyao, Tadahiro
2016-06-01
We present a general framework of Griffiths inequalities for quantum systems. Our approach is based on operator inequalities associated with self-dual cones and provides a consistent viewpoint of the Griffiths inequality. As examples, we discuss the quantum Ising model, quantum rotor model, Bose-Hubbard model, and Hubbard model. We present a model-independent structure that governs the correlation inequalities.
ERIC Educational Resources Information Center
Ortquist, Leslie
1989-01-01
Offers Alain Robbe-Grillet's novel "La Belle Captive" (which employs 77 paintings by the Belgian surrealist Rene Magritte) as playful interchange between word and image. Argues that the novel may be understood to demonstrate a fundamental relationship of inequality between word and image. (RS)
Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality
NASA Astrophysics Data System (ADS)
Roy, Arup; Sankar Bhattacharya, Some; Mukherjee, Amit; Banik, Manik
2015-10-01
We study a recently proposed Einstein-Podolsky-Rosen steering inequality (Cavalcanti et al 2015 J. Opt. Soc. Am. B 32 A74-A81). Analogous to Clauser-Horne-Shimony-Holt (CHSH) inequality for Bell nonlocality, in the simplest scenario, i.e., two parties, two measurements per party and two outcomes per measurement, this newly proposed inequality has been proved to be necessary and sufficient for steering. In this article we find the optimal violation amount of this inequality in quantum theory. Interestingly, the optimal violation amount matches with optimal quantum violation of CHSH inequality, i.e., Cirel’son quantity. We further study the optimal violation of this inequality for different classes of 2-qubit quantum states.
Branciard, Cyril
2011-03-15
A common problem in Bell-type experiments is the well-known detection loophole: if the detection efficiencies are not perfect and if one simply postselects the conclusive events, one might observe a violation of a Bell inequality, even though a local model could have explained the experimental results. In this paper, we analyze the set of all postselected correlations that can be explained by a local model, and show that it forms a polytope, larger than the Bell local polytope. We characterize the facets of this postselected local polytope in the Clauser-Horne-Shimony-Holt scenario, where two parties have binary inputs and outcomes. Our approach gives interesting insights on the detection loophole problem.
Improved Bell-in-a-Bell-Jar Demonstration
NASA Astrophysics Data System (ADS)
Han, Dejun
2003-05-01
It is well understood in acoustics that a medium is required to conduct sound. Stated in another way, sound is not transmitted through a vacuum. The earliest person to test this experimentally was the Irish physicist Robert Boyle (1627-1691). In his experiment, he put a ringing bell under a glass cover called a bell jar. After the air was pumped out, the ringing disappeared. This convinced him that sound cannot be conducted in vacuum. Here we describe an improved version of this demonstration.
Geometric Decompositions of Bell Polytopes with Practical Applications
NASA Astrophysics Data System (ADS)
Bierhorst, Peter
In the well-studied (2,2,2) Bell experiment consisting of two parties, two measurement settings per party, and two possible outcomes per setting, it is known that if the experiment obeys no-signaling constraints, then the set of admissible experimental probability distributions is fully characterized as the convex hull of 24 distributions: 8 Popescu-Rohrlich (PR) boxes and 16 local deterministic distributions. Here, we refine this result to show that in the (2,2,2) case, any nonlocal nonsignaling distribution can always be uniquely expressed as a convex combination of exactly one PR box and (up to) eight local deterministic distributions. In this representation each PR box will always occur only with a fixed set of eight local deterministic distributions with which it is affiliated. This decomposition has multiple applications: we demonstrate an analytical proof that the minimum detection efficiency for which nonlocality can be observed is 2/3 even for theories constrained only by the no-signaling principle, and we develop new algorithms that speed the calculation of important statistical functions of Bell test data. Finally, we enumerate the vertices of the no-signaling polytope for the (2, n, 2) ``chained Bell'' scenario and find that similar decomposition results are possible in this general case. Here, our results allow us to prove the optimality of a bound, derived in (Barrett et al., PRL, 2006) on the proportion of local theories in a local/nonlocal mixture that can be inferred from the experimental violation of a chained Bell inequality.
Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis.
Hensen, B; Kalb, N; Blok, M S; Dréau, A E; Reiserer, A; Vermeulen, R F L; Schouten, R N; Markham, M; Twitchen, D J; Goodenough, K; Elkouss, D; Wehner, S; Taminiau, T H; Hanson, R
2016-01-01
The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682-686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, in agreement with the first run, yielding an overall value of S = 2.38 ± 0.14. We calculate the resulting P-values of the second experiment and of the combined Bell tests. We provide an additional analysis of the distribution of settings choices recorded during the two tests, finding that the observed distributions are consistent with uniform settings for both tests. Finally, we analytically study the effect of particular models of random number generator (RNG) imperfection on our hypothesis test. We find that the winning probability per trial in the CHSH game can be bounded knowing only the mean of the RNG bias. This implies that our experimental result is robust for any model underlying the estimated average RNG bias, for random bits produced up to 690 ns too early by the random number generator. PMID:27509823
Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis
Hensen, B.; Kalb, N.; Blok, M. S.; Dréau, A. E.; Reiserer, A.; Vermeulen, R. F. L.; Schouten, R. N.; Markham, M.; Twitchen, D. J.; Goodenough, K.; Elkouss, D.; Wehner, S.; Taminiau, T. H.; Hanson, R.
2016-01-01
The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682–686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, in agreement with the first run, yielding an overall value of S = 2.38 ± 0.14. We calculate the resulting P-values of the second experiment and of the combined Bell tests. We provide an additional analysis of the distribution of settings choices recorded during the two tests, finding that the observed distributions are consistent with uniform settings for both tests. Finally, we analytically study the effect of particular models of random number generator (RNG) imperfection on our hypothesis test. We find that the winning probability per trial in the CHSH game can be bounded knowing only the mean of the RNG bias. This implies that our experimental result is robust for any model underlying the estimated average RNG bias, for random bits produced up to 690 ns too early by the random number generator. PMID:27509823
ERIC Educational Resources Information Center
Jensen, Arthur R.
1975-01-01
Some of the key problems of educational equality -- equality of opportunities and inequality of performance; individual differences vs. group differences, coping with group inequality -- are made explicit. (Author/KM)
NASA Technical Reports Server (NTRS)
1943-01-01
Bell P-39D Airacobra: After initially seeing duty in the Pacific and European theaters of operation, P-39s were supplanted, then replaced by the P-38, P-47 and P-51. Many of the Bell Fighters made their way to the Soviet Union, while others, like this P-39D, were used in the Unites States. This Airacobra was flown by the NACA in early 1943. Note the engine located in the middle of the fuselage, and the cannon in the propeller spinner.
Cinabro, David
2016-01-01
The major goals of our work on Belle II were to complete our contributions, a 64 channel PIN diode based radiation monitor, to the precursor detector called Beast II and the electronics for the endcap K-Long/Muon (E-KLM) detector. This was done by Professor Cinabro, Technician Gutierrez, and undergraduate labor supported by US-Japan funds. Professor Bonvicini through US-Japan funds led the development and installation of a beamstrahlung monitor system in the Belle II interaction region. Graduate students Farhat and DiCarlo worked on this. We also worked on charm physics analysis.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Bell Mountain. 9.55... Mountain. (a) Name. The name of the viticultural area described in this section is “Bell Mountain.” (b) Approved map. The appropriate map for determining the boundaries of the Bell Mountain viticultural area...
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Bell Mountain. 9.55... Mountain. (a) Name. The name of the viticultural area described in this section is “Bell Mountain.” (b) Approved map. The appropriate map for determining the boundaries of the Bell Mountain viticultural area...
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Bell Mountain. 9.55... Mountain. (a) Name. The name of the viticultural area described in this section is “Bell Mountain.” (b) Approved map. The appropriate map for determining the boundaries of the Bell Mountain viticultural area...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Bell Mountain. 9.55... Mountain. (a) Name. The name of the viticultural area described in this section is “Bell Mountain.” (b) Approved map. The appropriate map for determining the boundaries of the Bell Mountain viticultural area...
Code of Federal Regulations, 2014 CFR
2014-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Bell Mountain. 9.55... Mountain. (a) Name. The name of the viticultural area described in this section is “Bell Mountain.” (b) Approved map. The appropriate map for determining the boundaries of the Bell Mountain viticultural area...
Code of Federal Regulations, 2014 CFR
2014-07-01
... 33 Navigation and Navigable Waters 1 2014-07-01 2014-07-01 false Belle River. 117.424 Section 117... OPERATION REGULATIONS Specific Requirements Louisiana § 117.424 Belle River. The draw of the S70 bridge, mile 23.8 (Landside Route) near Belle River, shall open on signal; except that, from 10 p.m. to 6...
Code of Federal Regulations, 2011 CFR
2011-07-01
... 33 Navigation and Navigable Waters 1 2011-07-01 2011-07-01 false Belle River. 117.424 Section 117... OPERATION REGULATIONS Specific Requirements Louisiana § 117.424 Belle River. The draw of the S70 bridge, mile 23.8 (Landside Route) near Belle River, shall open on signal; except that, from 10 p.m. to 6...
Code of Federal Regulations, 2013 CFR
2013-07-01
... 33 Navigation and Navigable Waters 1 2013-07-01 2013-07-01 false Belle River. 117.424 Section 117... OPERATION REGULATIONS Specific Requirements Louisiana § 117.424 Belle River. The draw of the S70 bridge, mile 23.8 (Landside Route) near Belle River, shall open on signal; except that, from 10 p.m. to 6...
Code of Federal Regulations, 2012 CFR
2012-07-01
... 33 Navigation and Navigable Waters 1 2012-07-01 2012-07-01 false Belle River. 117.424 Section 117... OPERATION REGULATIONS Specific Requirements Louisiana § 117.424 Belle River. The draw of the S70 bridge, mile 23.8 (Landside Route) near Belle River, shall open on signal; except that, from 10 p.m. to 6...
Code of Federal Regulations, 2010 CFR
2010-07-01
... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Belle River. 117.424 Section 117... OPERATION REGULATIONS Specific Requirements Louisiana § 117.424 Belle River. The draw of the S70 bridge, mile 23.8 (Landside Route) near Belle River, shall open on signal; except that, from 10 p.m. to 6...
Graphing Inequalities, Connecting Meaning
ERIC Educational Resources Information Center
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
BELLE FOURCHE RIVER WATERSHED ASSESSMENT
The Belle Fourche River is a natural stream that drains portions of Butte, Lawrence, and Meade Counties in South Dakota and flows to the Cheyenne River in Meade County. The river receives runoff from agricultural operations and both the river and its tributaries have experienced...
ERIC Educational Resources Information Center
Houston, Paul
1996-01-01
Selfishness has spawned a new breed of racism, driven by fear, fed by scarcity, and manifested through economic imperatives. California's Proposition 187 and Herrnstein and Murray's book "The Bell Curve" are built on racist foundations. Our current obsession with race is driven by an economy and an elitist social system that is dismantling the…