Classicalquantum mixing in the random 2satisfiability problem
NASA Astrophysics Data System (ADS)
Potirniche, IonutDragos; Laumann, C. R.; Sondhi, S. L.
20151001
Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA, respectively, and they are believed to be intractable for both classical and quantum computers. Statistical ensembles of instances of these problems have been studied previously in an attempt to elucidate their typical, as opposed to worstcase, behavior. In this paper, we introduce a statistical ensemble that interpolates between classical and quantum. For the simplest 2SAT2QSAT ensemble, we find the exact boundary that separates SAT and UNSAT instances. We do so by establishing coincident lower and upper bounds, in the limit of large instances, on the extent of the UNSAT and SAT regions, respectively.
Mixed quantumclassical versus full quantum dynamics: Coupled quasiparticleoscillator system
NASA Astrophysics Data System (ADS)
Schanz, Holger; Esser, Bernd
19970501
The relation between the dynamical properties of a coupled quasiparticleoscillator system in the mixed quantumclassical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn amical BornOppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.
Mixed quantumclassical equilibrium in global flux surface hopping
Sifain, Andrew E.; Wang, Linjun; Prezhdo, Oleg V.
20150614
Global flux surface hopping (GFSH) generalizes fewest switches surface hopping (FSSH)—one of the most popular approaches to nonadiabatic molecular dynamics—for processes exhibiting superexchange. We show that GFSH satisfies detailed balance and leads to thermodynamic equilibrium with accuracy similar to FSSH. This feature is particularly important when studying electronvibrational relaxation and phononassisted transport. By studying the dynamics in a threelevel quantum system coupled to a classical atom in contact with a classical bath, we demonstrate that both FSSH and GFSH achieve the Boltzmann state populations. Thermal equilibrium is attained significantly faster with GFSH, since it accurately represents the superexchange process. GFSH converges closer to the Boltzmann averages than FSSH and exhibits significantly smaller statistical errors.
Dynamically consistent method for mixed quantumclassical simulations: A semiclassical approach
Antipov, Sergey V.; Ye, Ziyu; Ananth, Nandini
20150514
We introduce a new semiclassical (SC) framework, the Mixed QuantumClassical Initial Value Representation (MQCIVR), that can be tuned to reproduce existing quantumlimit and classicallimit SC approximations to quantum realtime correlation functions. Applying a modified Filinov transformation to a quantumlimit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQCIVR expression provides a consistent dynamic framework for mixed quantumclassical simulations and we demonstrate its numerical accuracy in the calculation of realtime correlation functions for a model 1D system and a model 2D system over the full range of quantum to classicallimit behaviors.
Dynamically consistent method for mixed quantumclassical simulations: A semiclassical approach
NASA Astrophysics Data System (ADS)
Antipov, Sergey V.; Ye, Ziyu; Ananth, Nandini
20150501
We introduce a new semiclassical (SC) framework, the Mixed QuantumClassical Initial Value Representation (MQCIVR), that can be tuned to reproduce existing quantumlimit and classicallimit SC approximations to quantum realtime correlation functions. Applying a modified Filinov transformation to a quantumlimit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQCIVR expression provides a consistent dynamic framework for mixed quantumclassical simulations and we demonstrate its numerical accuracy in the calculation of realtime correlation functions for a model 1D system and a model 2D system over the full range of quantum to classicallimit behaviors.
Shakib, Farnaz; Hanna, Gabriel
20160712
In this work, we derive a general mixed quantumclassical formula for calculating thermal protoncoupled electrontransfer (PCET) rate constants, starting from the time integral of the quantum fluxflux correlation function. This formula allows for the direct simulation of PCET reaction dynamics via the mixed quantumclassical Liouville approach. Owing to the general nature of the derivation, this formula does not rely on any prior mechanistic assumptions and can be applied across a wide range of electronic and protonic coupling regimes. To test the validity of this formula, we applied it to a reduced model of a condensedphase PCET reaction. Good agreement with the numerically exact rate constant is obtained, demonstrating the accuracy of our formalism. We believe that this approach constitutes a solid foundation for future investigations of the rates and mechanisms of a wide range of PCET reactions. PMID:27232936
NASA Astrophysics Data System (ADS)
Schubert, Alexander; Falvo, Cyril; Meier, Christoph
20160801
We present mixed quantumclassical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the "surfaces" for the classical trajectories of protein and solvent atoms. In return, environmentally induced nonadiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking the molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket.
Schubert, Alexander; Falvo, Cyril; Meier, Christoph
20160801
We present mixed quantumclassical simulations on relaxation and dephasing of vibrationally excited carbon monoxide within a protein environment. The methodology is based on a vibrational surface hopping approach treating the vibrational states of CO quantum mechanically, while all remaining degrees of freedom are described by means of classical molecular dynamics. The CO vibrational states form the "surfaces" for the classical trajectories of protein and solvent atoms. In return, environmentally induced nonadiabatic couplings between these states cause transitions describing the vibrational relaxation from first principles. The molecular dynamics simulation yields a detailed atomistic picture of the energy relaxation pathways, taking the molecular structure and dynamics of the protein and its solvent fully into account. Using the ultrafast photolysis of CO in the hemoprotein FixL as an example, we study the relaxation of vibrationally excited CO and evaluate the role of each of the FixL residues forming the heme pocket. PMID:27497540
Semenov, Alexander; Babikov, Dmitri
20150521
An efficient and accurate mixed quantum/classical theory approach for computational treatment of inelastic scattering is extended to describe collision of an atom with a general asymmetrictop rotor polyatomic molecule. Quantum mechanics, employed to describe transitions between the internal states of the molecule, and classical mechanics, employed for description of scattering of the atom, are used in a selfconsistent manner. Such calculations for rotational excitation of HCOOCH3 in collisions with He produce accurate results at scattering energies above 15 cm(1), although resonances near threshold, below 5 cm(1), cannot be reproduced. Importantly, the method remains computationally affordable at high scattering energies (here up to 1000 cm(1)), which enables calculations for larger molecules and at higher collision energies than was possible previously with the standard fullquantum approach. Theoretical prediction of inelastic cross sections for a number of complex organic molecules observed in space becomes feasible using this new computational tool. PMID:26263260
Gelman, David; Schwartz, Steven D.
20080714
The recently developed mixed quantumclassical propagation method is extended to treat tunneling effects in multidimensional systems. Formulated for systems consisting of a quantum primary part and a classical bath of heavier particles, the method employs a frozen Gaussian description for the bath degrees of freedom, while the dynamics of the quantum subsystem is governed by a corrected propagator. The corrections are defined in terms of matrix elements of zerothorder propagators. The method is applied to a model system of a doublewell potential bilinearly coupled to a harmonic oscillator. The extension of the method, which includes nondiagonal elements of the correction propagator, enables an accurate treatment of tunneling in an antisymmetric doublewell potential.
Mixed QuantumClassical Study of Nonadiabatic Curve Crossing in Condensed Phases.
Xie, Weiwei; Xu, Meng; Bai, Shuming; Shi, Qiang
20160519
We apply the mixed quantumclassical Liouville (MQCL) equation to investigate the nonadiabatic curve crossing in condensed phases. More specifically, electron transfer rate constants of the spinBoson model are calculated by employing a rate constant expression using the collective solvent polarization as the reaction coordinate. In the calculation, classical nuclear degrees of freedom are initially sampled at the transition state configuration, and the initial state for the electronic degree of freedom is obtained from a mixed quantumclassical Boltzmann distribution. Different contributions to the electron transfer rate from the diagonal and offdiagonal elements of the initial density matrix, and contributions from trajectories with positive and negative initial velocities are analyzed. It is shown that the offdiagonal elements of the initial density matrix play an important role in the total electron transfer rate. The MQCL results are also compared with those calculated using Ehrenfest dynamics. It is found that, although the Ehrenfest dynamics is inaccurate when the reactive flux rate expression is used directly, it can give reasonably accurate results when individual contributions from the diagonal and offdiagonal elements of the initial density matrix are calculated. PMID:26840040
Ryabinkin, Ilya G; Nagesh, Jayashree; Izmaylov, Artur F
20151101
We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the timederivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantumclassical methods using numerical differentiation of electronic wave functions in the Slater determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals and then to apply a finitedifference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive severalorderofmagnitude speedups of the TDNAC calculation step for midsize molecules. PMID:26538034
Babikov, Dmitri; Semenov, Alexander
20160128
A mixed quantum/classical approach to inelastic scattering (MQCT) is developed in which the relative motion of two collision partners is treated classically, and the rotational and vibrational motion of each molecule is treated quantum mechanically. The cases of molecule + atom and molecule + molecule are considered including diatomics, symmetrictop rotors, and asymmetrictop rotor molecules. Phase information is taken into consideration, permitting calculations of elastic and inelastic, total and differential cross sections for excitation and quenching. The method is numerically efficient and intrinsically parallel. The scaling law of MQCT is favorable, which enables calculations at high collision energies and for complicated molecules. Benchmark studies are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates that MQCT is a viable approach to inelastic scattering. At higher collision energies it can confidently replace the computationally expensive fullquantum calculations. At low collision energies and for lowmass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with fullquantum calculations at low energies. PMID:26618533
Ivanov, Mikhail V; Babikov, Dmitri
20110414
A mixed quantumclassical approach to the description of collisional energy transfer is proposed in which the vibrational motion of an energized molecule is treated quantum mechanically using wave packets, while the collisional motion of the molecule and quencher and the rotational motion of the molecule are treated using classical trajectories. This accounts rigorously for quantization of vibrational states, zeropoint energy, scattering resonances, and permutation symmetry of identical atoms, while advantage is taken of the classical scattering regime. Energy is exchanged between vibrational, rotational, and translational degrees of freedom while the total energy is conserved. Application of this method to stabilization of the van der Waals states in ozone is presented. Examples of mixed quantumclassical trajectories are discussed, including an interesting example of supercollision. When combined with an efficient grid mapping procedure and the reduced dimensionality approximation, the method becomes very affordable computationally. PMID:21495742
Megow, Jörg
20151001
The computation of dispersive site energy shifts due to van der Waals interaction (London dispersion forces) was combined with mixed quantumclassical methodology to calculate the linear optical absorption spectra of large pheophorbide a (Pheo) dendrimers. The computed spectra agreed very well with the measurements considering three characteristic optical features occurring with increasing aggregate size: a strong line broadening, a redshift, and a lowenergy shoulder. The improved mixed quantumclassical methodology is considered a powerful tool in investigating molecular aggregates. PMID:26275373
Ivanov, Mikhail; Dubernet, MarieLise; Babikov, Dmitri
20140407
The mixed quantum/classical theory (MQCT) formulated in the spacefixed reference frame is used to compute quenching cross sections of several rotationally excited states of water molecule by impact of He atom in a broad range of collision energies, and is tested against the fullquantum calculations on the same potential energy surface. In current implementation of MQCT method, there are two major sources of errors: one affects results at energies below 10 cm{sup −1}, while the other shows up at energies above 500 cm{sup −1}. Namely, when the collision energy E is below the statetostate transition energy ΔE the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the averagevelocity principle (scaling of collision energy in order to satisfy microscopic reversibility) helps dramatically. At higher energies, MQCT is expected to be accurate but in current implementation, in order to make calculations computationally affordable, we had to cut off the basis set size. This can be avoided by using a more efficient bodyfixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the fullquantum results almost everywhere through fourordersofmagnitude range of collision energies, except near resonances, where the errors are somewhat larger.
Ivanov, Mikhail; Dubernet, MarieLise; Babikov, Dmitri
20140401
The mixed quantum/classical theory (MQCT) formulated in the spacefixed reference frame is used to compute quenching cross sections of several rotationally excited states of water molecule by impact of He atom in a broad range of collision energies, and is tested against the fullquantum calculations on the same potential energy surface. In current implementation of MQCT method, there are two major sources of errors: one affects results at energies below 10 cm(1), while the other shows up at energies above 500 cm(1). Namely, when the collision energy E is below the statetostate transition energy ΔE the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the averagevelocity principle (scaling of collision energy in order to satisfy microscopic reversibility) helps dramatically. At higher energies, MQCT is expected to be accurate but in current implementation, in order to make calculations computationally affordable, we had to cut off the basis set size. This can be avoided by using a more efficient bodyfixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the fullquantum results almost everywhere through fourordersofmagnitude range of collision energies, except near resonances, where the errors are somewhat larger. PMID:24712787
On the equivalence between nonfactorizable mixedstrategy classical games and quantum games
Iqbal, Azhar; Chappell, James M.; Abbott, Derek
20160101
A gametheoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question is to understand the conditions under which a classical gametheoretic setting can be transformed to a quantum game, and under which conditions there is an equivalence. In this paper, we consider quantum games as those that allow nonfactorizable probabilities. We discuss two approaches for obtaining a nonfactorizable game and study the outcome of such games. We demonstrate how the standard version of a quantum game can be analysed as a nonfactorizable game and determine the limitations of our approach. PMID:26909174
Xie, Weiwei; Xu, Yang; Zhu, Lili; Shi, Qiang
20140507
We present mixed quantum classical calculations of the proton transfer (PT) reaction rates represented by a double well system coupled to a dissipative bath. The rate constants are calculated within the so called nontraditional view of the PT reaction, where the proton motion is quantized and the solvent polarization is used as the reaction coordinate. Quantization of the proton degree of freedom results in a problem of nonadiabatic dynamics. By employing the reactive flux formulation of the rate constant, the initial sampling starts from the transition state defined using the collective reaction coordinate. Dynamics of the collective reaction coordinate is treated classically as over damped diffusive motion, for which the equation of motion can be derived using the path integral, or the mixed quantum classical Liouville equation methods. The calculated mixed quantum classical rate constants agree well with the results from the numerically exact hierarchical equation of motion approach for a broad range of model parameters. Moreover, we are able to obtain contributions from each vibrational state to the total reaction rate, which helps to understand the reaction mechanism from the deep tunneling to over the barrier regimes. The numerical results are also compared with those from existing approximate theories based on calculations of the nonadiabatic transmission coefficients. It is found that the twosurface LandauZener formula works well in calculating the transmission coefficients in the deep tunneling regime, where the crossing point between the two lowest vibrational states dominates the total reaction rate. When multiple vibrational levels are involved, including additional crossing points on the free energy surfaces is important to obtain the correct reaction rate using the LandauZener formula.
Xie, Weiwei; Xu, Yang; Zhu, Lili; Shi, Qiang
20140501
We present mixed quantum classical calculations of the proton transfer (PT) reaction rates represented by a double well system coupled to a dissipative bath. The rate constants are calculated within the so called nontraditional view of the PT reaction, where the proton motion is quantized and the solvent polarization is used as the reaction coordinate. Quantization of the proton degree of freedom results in a problem of nonadiabatic dynamics. By employing the reactive flux formulation of the rate constant, the initial sampling starts from the transition state defined using the collective reaction coordinate. Dynamics of the collective reaction coordinate is treated classically as over damped diffusive motion, for which the equation of motion can be derived using the path integral, or the mixed quantum classical Liouville equation methods. The calculated mixed quantum classical rate constants agree well with the results from the numerically exact hierarchical equation of motion approach for a broad range of model parameters. Moreover, we are able to obtain contributions from each vibrational state to the total reaction rate, which helps to understand the reaction mechanism from the deep tunneling to over the barrier regimes. The numerical results are also compared with those from existing approximate theories based on calculations of the nonadiabatic transmission coefficients. It is found that the twosurface LandauZener formula works well in calculating the transmission coefficients in the deep tunneling regime, where the crossing point between the two lowest vibrational states dominates the total reaction rate. When multiple vibrational levels are involved, including additional crossing points on the free energy surfaces is important to obtain the correct reaction rate using the LandauZener formula. PMID:24811623
NASA Astrophysics Data System (ADS)
Suzuki, Yasumitsu; Watanabe, Kazuyuki; Abedi, Ali; Agostini, Federica; Min, Seung Kyu; Maitra, Neepa; Gross, E. K. U.
The exact factorization of the electronnuclear wave function allows to define the timedependent potential energy surfaces (TDPESs) responsible for the nuclear dynamics and electron dynamics. Recently a novel coupledtrajectory mixed quantumclassical (CTMQC) approach based on this TDPES has been developed, which accurately reproduces both nuclear and electron dynamics. Here we study the TDPES for laserinduced electron localization with a view to developing a MQC method for strongfield processes. We show our recent progress in applying the CTMQC approach to the systems with many degrees of freedom.
Wang Linjun; Beljonne, David; Chen Liping; Shi Qiang
20110628
The electronphonon coupling is critical in determining the intrinsic charge carrier and exciton transport properties in organic materials. In this study, we consider a SuSchriefferHeeger (SSH) model for molecular crystals, and perform numerical benchmark studies for different strategies of simulating the mixed quantumclassical dynamics. These methods, which differ in the selection of initial conditions and the representation used to solve the time evolution of the quantum carriers, are shown to yield similar equilibrium diffusion properties. A hybrid approach combining molecular dynamics simulations of nuclear motion and quantumchemical calculations of the electronic Hamiltonian at each geometric configuration appears as an attractive strategy to model charge dynamics in large size systems ''on the fly,'' yet it relies on the assumption that the quantum carriers do not impact the nuclear dynamics. We find that such an approximation systematically results in overestimated chargecarrier mobilities, with the associated error being negligible when the roomtemperature mobility exceeds {approx}4.8 cm{sup 2}/Vs ({approx}0.14 cm{sup 2}/Vs) in onedimensional (twodimensional) crystals.
Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu
20140828
In order to investigate proton transfer reaction in solution, mixed quantumclassical molecular dynamics calculations have been carried out based on our previously proposed quantum equation of motion for the reacting system [A. Yamada and S. Okazaki, J. Chem. Phys. 128, 044507 (2008)]. Surface hopping method was applied to describe forces acting on the solvent classical degrees of freedom. In a series of our studies, quantum and solvent effects on the reaction dynamics in solutions have been analysed in detail. Here, we report our mixed quantumclassical molecular dynamics calculations for intramolecular proton transfer of malonaldehyde in water. Thermally activated proton transfer process, i.e., vibrational excitation in the reactant state followed by transition to the product state and vibrational relaxation in the product state, as well as tunneling reaction can be described by solving the equation of motion. Zero point energy is, of course, included, too. The quantum simulation in water has been compared with the fully classical one and the wave packet calculation in vacuum. The calculated quantum reaction rate in water was 0.70 ps{sup −1}, which is about 2.5 times faster than that in vacuum, 0.27 ps{sup −1}. This indicates that the solvent water accelerates the reaction. Further, the quantum calculation resulted in the reaction rate about 2 times faster than the fully classical calculation, which indicates that quantum effect enhances the reaction rate, too. Contribution from three reaction mechanisms, i.e., tunneling, thermal activation, and barrier vanishing reactions, is 33:46:21 in the mixed quantumclassical calculations. This clearly shows that the tunneling effect is important in the reaction.
Semenov, Alexander; Babikov, Dmitri
20160601
Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantummechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the statetostate transition cross sections are compared versus those obtained from the fullquantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact fullquantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes. PMID:27187769
Subnuclear realm: classical in quantum and quantum in classical
Kosyakov, B. P.
19990311
Exact solutions in the classical YangMillsWong theory enable explaining a number of enigmatic classical features of subnuclear realm. Moreover, they reveal some unexpected quantum features of this classical treatment.
Computational quantumclassical boundary of noisy commuting quantum circuits.
Fujii, Keisuke; Tamate, Shuhei
20160101
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantumclassical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurementbased quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projectedentangledpairstate picture and the GottesmanKnill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a singlequbit completepositivetracepreserving noise, the computational quantumclassical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantumclassical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039
Computational quantumclassical boundary of noisy commuting quantum circuits
Fujii, Keisuke; Tamate, Shuhei
20160101
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantumclassical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurementbased quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projectedentangledpairstate picture and the GottesmanKnill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a singlequbit completepositivetracepreserving noise, the computational quantumclassical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantumclassical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039
Computational quantumclassical boundary of noisy commuting quantum circuits
NASA Astrophysics Data System (ADS)
Fujii, Keisuke; Tamate, Shuhei
20160501
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantumclassical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurementbased quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projectedentangledpairstate picture and the GottesmanKnill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a singlequbit completepositivetracepreserving noise, the computational quantumclassical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantumclassical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.
Quantum Computing's Classical Problem, Classical Computing's Quantum Problem
NASA Astrophysics Data System (ADS)
Van Meter, Rodney
20140801
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediatescale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantum computing systems that outcompute classical systems capable of some logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends.
Quantum transitions between classical histories
NASA Astrophysics Data System (ADS)
Hartle, James; Hertog, Thomas
20150901
In a quantum theory of gravity spacetime behaves classically when quantum probabilities are high for histories of geometry and field that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This quantum perspective on classicality has important implications. (a) Classical histories are generally available only in limited patches of the configuration space on which the state lives. (b) In a given patch, states generally predict relative probabilities for an ensemble of possible classical histories. (c) In between patches classical predictability breaks down and is replaced by quantum evolution connecting classical histories in different patches. (d) Classical predictability can break down on scales well below the Planck scale, and with no breakdown in the classical equations of motion. We support and illustrate (a)(d) by calculating the quantum transition across the de Sitterlike throat connecting asymptotically classical, inflating histories in the noboundary quantum state. This supplies probabilities for how a classical history on one side transitions and branches into a range of classical histories on the opposite side. We also comment on the implications of (a)(d) for the dynamics of black holes and eternal inflation.
NASA Astrophysics Data System (ADS)
Sbisà, Fulvio
20150101
The aim of these notes is to provide a selfcontained review of why it is generically a problem when a solution of a theory possesses ghost fields among the perturbation modes. We define what a ghost field is and we show that its presence is associated with a classical instability whenever the ghost field interacts with standard fields. We then show that the instability is more severe at quantum level, and that perturbative ghosts can exist only in low energy effective theories. However, if we do not consider very ad hoc choices, compatibility with observational constraints implies that low energy effective ghosts can exist only at the price of giving up Lorentz invariance or locality above the cutoff, in which case the cutoff has to be much lower that the energy scales we currently probe in particle colliders. We also comment on the possible role of extra degrees of freedom which break Lorentz invariance spontaneously.
Quantum money with classical verification
Gavinsky, Dmitry
20141204
We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. Our scheme is secure against adaptive adversaries  this property is not directly related to the possibility of classical verification, nevertheless none of the earlier quantum money constructions is known to possess it.
Quantum money with classical verification
NASA Astrophysics Data System (ADS)
Gavinsky, Dmitry
20141201
We propose and construct a quantum money scheme that allows verification through classical communication with a bank. This is the first demonstration that a secure quantum money scheme exists that does not require quantum communication for coin verification. Our scheme is secure against adaptive adversaries  this property is not directly related to the possibility of classical verification, nevertheless none of the earlier quantum money constructions is known to possess it.
Classicality of a quantum oscillator
NASA Astrophysics Data System (ADS)
Ahmadzadegan, Aida; Mann, Robert B.; Terno, Daniel R.
20160301
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. By using both the Hilbert space (Koopman) and the phasespace (Moyal) formalisms we investigate how robust this classicality is. We find failures of consistency of the dynamics of hybrid classicalquantum systems from both perspectives. By demanding that no unobservable operators couple to the quantum sector in the Koopmanian formalism, we show that the classical equations of motion act on their quantum counterparts without experiencing any back reaction, resulting in nonconservation of energy in the quantum system. By using the phasespace formalism we study the shorttime evolution of the moment equations of a hybrid classicalGaussian quantum system and observe violations of the Heisenberg uncertainty relation in the quantum sector for a broad range of initial conditions. We estimate the timescale for these violations, which is generically rather short. This inconsistency indicates that while many explicitly quantum effects can be represented classically, quantum aspects of the system cannot be fully masked. We comment on the implications of our results for quantum gravity.
Semenov, Alexander; Babikov, Dmitri
20151217
The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the moleculemolecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the meanfield potential. Numerical tests of this theory are carried out for several most important rotational statetostate transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with fullquantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the fullquantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetrictop rotor (polyatomic) molecules are relatively straightforward. PMID:26323089
Quantum mechanics from classical statistics
Wetterich, C.
20100415
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics  the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the noncommuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.
Classical versus quantum completeness
NASA Astrophysics Data System (ADS)
Hofmann, Stefan; Schneider, Marc
20150601
The notion of quantummechanical completeness is adapted to situations where the only adequate description is in terms of quantum field theory in curved spacetimes. It is then shown that Schwarzschild black holes, although geodesically incomplete, are quantum complete.
Quantum localization of classical mechanics
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
20160701
Quantum localization of classical mechanics within the BRSTBFV and BV (or fieldantifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRSTBFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRSTBFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial nondegenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Classical dynamics of quantum entanglement.
Casati, Giulio; Guarneri, Italo; Reslen, Jose
20120301
We analyze numerically the dynamical generation of quantum entanglement in a system of two interacting particles, started in a coherent separable state, for decreasing values of ℏ. As ℏ→0 the entanglement entropy, computed at any finite time, converges to a finite nonzero value. The limit law that rules the time dependence of entropy is well reproduced by purely classical computations. Its general features can be explained by simple classical arguments, which expose the different ways entanglement is generated in systems that are classically chaotic or regular. PMID:22587162
Classical communication cost of quantum steering
NASA Astrophysics Data System (ADS)
Sainz, Ana Belén; Aolita, Leandro; Brunner, Nicolas; Gallego, Rodrigo; Skrzypczyk, Paul
20160701
Quantum steering is observed when performing appropriate local measurements on an entangled state. Here we discuss the possibility of simulating classically this effect, using classical communication instead of entanglement. We show that infinite communication is necessary for exactly simulating steering for any pure entangled state, as well as for a class of mixed entangled states. Moreover, we discuss the communication cost of steering for general entangled states, as well as approximate simulation. Our findings reveal striking differences between Bell nonlocality and steering and provide a natural way of measuring the strength of the latter.
Quantum remnants in the classical limit
NASA Astrophysics Data System (ADS)
Kowalski, A. M.; Plastino, A.
20160901
We analyze here the common features of two dynamical regimes: a quantum and a classical one. We deal with a well known semiclassic system in its route towards the classical limit, together with its purely classic counterpart. We wish to ascertain i) whether some quantum remnants can be found in the classical limit and ii) the details of the quantumclassic transition. The socalled mutual information is the appropriate quantifier for this task. Additionally, we study the BandtPompe's symbolic patterns that characterize dynamical time series (representative of the semiclassical system under scrutiny) in their evolution towards the classical limit.
Classical Concepts in Quantum Programming
NASA Astrophysics Data System (ADS)
Ömer, Bernhard
20050701
The rapid progress of computer technology has been accompanied by a corresponding evolution of software development, from hardwired components and binary machine code to high level programming languages, which allowed to master the increasing hardware complexity and fully exploit its potential. This paper investigates, how classical concepts like hardware abstraction, hierarchical programs, data types, memory management, flow of control, and structured programming can be used in quantum computing. The experimental language QCL will be introduced as an example, how elements like irreversible functions, local variables, and conditional branching, which have no direct quantum counterparts, can be implemented, and how nonclassical features like the reversibility of unitary transformation or the nonobservability of quantum states can be accounted for within the framework of a procedural programming language.
Classical analog of quantum phase
Ord, G.N.
19920701
A modified version of the Feynman relativistic chessboard model (FCM) is investigated in which the paths involved are spirals in the spacetime. Portions of the paths in which the particle`s proper time is reversed are interpreted in terms of antiparticles. With this intepretation the particleantiparticle field produced by such trajectories provides a classical analog of the phase associated with particle paths in the unmodified FCM. It is shwon that in the nonrelativistic limit the resulting kernel is the correct Dirac propagator and that particleantiparticle symmetry is in this case responsible for quantum interference. 7 refs., 3 figs.
Classical oscillators in the control of quantum tunneling: Numerical experiments
NASA Astrophysics Data System (ADS)
Kar, Susmita; Bhattacharyya, S. P.
20160601
The dynamics of a classical anharmonic oscillator is exploited to control the tunneling dynamics of a quantum particle to which the classical oscillator is coupled. The mixed quantum classical problem is investigated at a meanfield like level. The anharmonic strength (λ) , particle mass (Mc) and harmonic stiffness (ωc) of the classical controller are explored as possible control parameters for the tunneling dynamics. The strength, the type of coupling between the quantum system and classical controller and the effective frequency of the controller emerge as crucial factors in shaping the nature and extent of the control. A whole spectrum of possibilities starting from enhancement, suppression to complete destruction of tunneling emerge depending on values assigned to the control parameters, the type of coupling and the control configuration used. When classical controller is replaced by a quantum controller, the control landscape becomes much simpler.
BedardHearn, Michael J.; Larsen, Ross E.; Schwartz, Benjamin J.
20061121
Motivated by recent ultrafast spectroscopic experiments [Martini et al., Science 293, 462 (2001)], which suggest that photoexcited solvated electrons in tetrahydrofuran (THF) can relocalize (that is, return to equilibrium in solvent cavities far from where they started), we performed a series of nonequilibrium, nonadiabatic, mixed quantum/classical molecular dynamics simulations that mimic onephoton excitation of the THFsolvated electron. We find that as photoexcited THFsolvated electrons relax to their ground states either by continuous mixing from the excited state or via nonadiabatic transitions, {approx}30% of them relocalize into cavities that can be over 1 nm away from where they originated, in close agreement with the experiments. A detailed investigation shows that the ability of excited THFsolvated electrons to undergo photoinduced relocalization stems from the existence of preexisting cavity traps that are an intrinsic part of the structure of liquid THF. This explains why solvated electrons can undergo photoinduced relocalization in solvents like THF but not in solvents like water, which lack the preexisting traps necessary to stabilize the excited electron in other places in the fluid. We also find that even when they do not ultimately relocalize, photoexcited solvated electrons in THF temporarily visit other sites in the fluid, explaining why the photoexcitation of THFsolvated electrons is so efficient at promoting recombination with nearby scavengers. Overall, our study shows that the defining characteristic of a liquid that permits the photoassisted relocalization of solvated electrons is the existence of nascent cavities that are attractive to an excess electron; we propose that other such liquids can be found from classical computer simulations or neutron diffraction experiments.
Racing in parallel: Quantum versus Classical
NASA Astrophysics Data System (ADS)
Steiger, Damian S.; Troyer, Matthias
In a fair comparison of the performance of a quantum algorithm to a classical one it is important to treat them on equal footing, both regarding resource usage and parallelism. We show how one may otherwise mistakenly attribute speedup due to parallelism as quantum speedup. We apply such an analysis both to analog quantum devices (quantum annealers) and gate model algorithms and give several examples where a careful analysis of parallelism makes a significant difference in the comparison between classical and quantum algorithms.
Secure quantum communication using classical correlated channel
NASA Astrophysics Data System (ADS)
Costa, D.; de Almeida, N. G.; VillasBoas, C. J.
20160701
We propose a secure protocol to send quantum information from one part to another without a quantum channel. In our protocol, which resembles quantum teleportation, a sender (Alice) and a receiver (Bob) share classical correlated states instead of EPR ones, with Alice performing measurements in two different bases and then communicating her results to Bob through a classical channel. Our secure quantum communication protocol requires the same amount of classical bits as the standard quantum teleportation protocol. In our scheme, as in the usual quantum teleportation protocol, once the classical channel is established in a secure way, a spy (Eve) will never be able to recover the information of the unknown quantum state, even if she is aware of Alice's measurement results. Security, advantages, and limitations of our protocol are discussed and compared with the standard quantum teleportation protocol.
Mixed quantumclassical dynamics of an amideI vibrational excitation in a protein α helix
NASA Astrophysics Data System (ADS)
Freedman, Holly; Martel, Paulo; Cruzeiro, Leonor
20101101
Adenosine triphosphate (ATP) is known to be the main energy currency of the living cell, and is used as a coenzyme to generate energy for many cellular processes through hydrolysis to adenosine diphosphate (ADP), although the mechanism of energy transfer is not well understood. It has been proposed that following hydrolysis of the ATP cofactor bound to a protein, up to two quanta of amideI vibrational energy are excited and utilized to bring about important structural changes in the protein. To study whether, and how, amideI vibrational excitations are capable of leading to protein structural changes, we have added components arising from quantummechanical amideI vibrational excitations to the total energy and force terms within a moleculardynamics simulation. This model is applied to helical decaalanine as a test case to investigate how its dynamics differs in the presence or absence of an amideI excitation. We find that the presence of an amideI excitation can bias the structure toward a more helical state.
NASA Astrophysics Data System (ADS)
Yamashita, Takefumi; Takatsuka, Kazuo
20070201
The infrared spectrum of phenolwater cationic cluster, [PhOH•H2O]+, taken by Sawamura et al. [J. Phys. Chem. 100, 8131 (1996)] is puzzling in that the peak due to the stretching mode of the phenolic OH (3657cm1 for a neutral monomer and 3524cm1 for PhOH•H2O) seemingly disappears and instead an extremely broad tail extending down to 2900cm1 is observed. The present authors theoretically ascribe this anomalous spectrum to an inhomogeneous broadening of the OH stretching peak caused by the hydrogen bond, the strength of which has been greatly enhanced by ionization of the phenyl ring. Indeed they estimate that the peak position is at 2300cm1 and the spectral width can become as wide as 1000cm1 at the cluster energy of 32kcal/mol. This surprisingly wide broadening can be generic in hydrogenbond systems, which in turn is useful to study the nature of the hydrogenbond assisted dynamics in various systems such as those in DNA and proteins. To study the present system quantitatively, the authors have developed an ab initio mixed quantumclassical method, in which the nuclear motions on an adiabatic ab initio potential surface are treated such that only the OH stretching motion is described quantum mechanically, while all the other remaining modes are treated classically with onthefly scheme. This method includes the implementation of many numerical methodologies, which enables it to deal with a relatively large molecular system. With this theoretical method, the authors analyze the present anomalous broadening in a great detail. In particular, they suggest that one can extract direct information about the hydrogenbond dynamics with respect to the clear correlation between the vibrational excitation energy of the OH stretching and intermolecular distance by means of a timeresolved infrared spectroscopy: Reflecting the slow and widerange variation of the intermolecular distance of the relevant hydrogen bond, the timeresolved spectrum is predicted to vary
NASA Astrophysics Data System (ADS)
Shakib, Farnaz A.; Hanna, Gabriel
20160101
In a previous study [F. A. Shakib and G. Hanna, J. Chem. Phys. 141, 044122 (2014)], we investigated a model protoncoupled electron transfer (PCET) reaction via the mixed quantumclassical Liouville (MQCL) approach and found that the trajectories spend the majority of their time on the mean of two coherently coupled adiabatic potential energy surfaces. This suggested a need for mean surface evolution to accurately simulate observables related to ultrafast PCET processes. In this study, we simulate the timedependent populations of the three lowest adiabatic states in the ETPT (i.e., electron transfer preceding proton transfer) version of the same PCET model via the MQCL approach and compare them to the exact quantum results and those obtained via the fewest switches surface hopping (FSSH) approach. We find that the MQCL population profiles are in good agreement with the exact quantum results and show a significant improvement over the FSSH results. All of the mean surfaces are shown to play a direct role in the dynamics of the state populations. Interestingly, our results indicate that the population transfer to the secondexcited state can be mediated by dynamics on the mean of the ground and secondexcited state surfaces, as part of a sequence of nonadiabatic transitions that bypasses the firstexcited state surface altogether. This is made possible through nonadiabatic transitions between different mean surfaces, which is the manifestation of coherence transfer in MQCL dynamics. We also investigate the effect of the strength of the coupling between the proton/electron and the solvent coordinate on the state population dynamics. Drastic changes in the population dynamics are observed, which can be understood in terms of the changes in the potential energy surfaces and the nonadiabatic couplings. Finally, we investigate the state population dynamics in the PTET (i.e., proton transfer preceding electron transfer) and concerted versions of the model. The PT
Classical data compression with quantum side information
Devetak, I.; Winter, A.
20031001
The problem of classical data compression when the decoder has quantum side information at his disposal is considered. This is a quantum generalization of the classical SlepianWolf theorem. The optimal compression rate is found to be reduced from the Shannon entropy of the source by the Holevo information between the source and side information.
Dynamics in the quantum/classical limit based on selective use of the quantum potential.
Garashchuk, Sophya; Dell'Angelo, David; Rassolov, Vitaly A
20141221
A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the timedependent Schrödinger equation. The quantum potential is a nonlocal quantity, defined in the trajectorybased form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantummechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed "quantum," defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or meanfield, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and doublewell potentials, using conventional gridbased and approximate quantumtrajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction. PMID:25527919
Dynamics in the quantum/classical limit based on selective use of the quantum potential
Garashchuk, Sophya Dell’Angelo, David; Rassolov, Vitaly A.
20141221
A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the timedependent Schrödinger equation. The quantum potential is a nonlocal quantity, defined in the trajectorybased form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantummechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or meanfield, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and doublewell potentials, using conventional gridbased and approximate quantumtrajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction.
NASA Astrophysics Data System (ADS)
Glover, William J.; Larsen, Ross E.; Schwartz, Benjamin J.
20100401
We introduce an efficient multielectron firstprinciples based electronic structure method, the twoelectron Fouriergrid (2EFG) approach, that is particularly suited for use in mixed quantum/classical simulations of condensedphase systems. The 2EFG method directly solves for the sixdimensional wave function of a twoelectron Hamiltonian in a Fouriergrid representation such that the effects of electron correlation and exchange are treated exactly for both the ground and excited states. Due to the simplicity of a Fouriergrid representation, the 2EFG is readily parallelizable and we discuss its computational implementation in a distributedmemory parallel environment. We show our method is highly efficient, being able to find twoelectron wave functions in ˜20 s on a modern desktop computer for a calculation this is equivalent to full configuration interaction (FCI) in a basis of 17 million Slater determinants. We benchmark the accuracy of the 2EFG by applying it to two electronic structure test problems: the harmonium atom and the sodium dimer. We find that even with a modest grid basis size, our method converges to the analytically exact solutions of harmonium in both the weakly and strongly correlated electron regimes. Our method also reproduces the lowlying potential energy curves of the sodium dimer to a similar level of accuracy as a valence CI calculation, thus demonstrating its applicability to molecular systems. In the following paper [W. J. Glover, R. E. Larsen, and B. J. Schwartz, J. Chem. Phys. 132, 144102 (2010)], we use the 2EFG method to explore the nature of the electronic states that comprise the chargetransfertosolvent absorption band of sodium anions in liquid tetrahydrofuran.
Entropic inequalities in classical and quantum domains
NASA Astrophysics Data System (ADS)
Man'ko, Margarita A.
20100901
Different kinds of entropy associated with probability distribution functions characterizing the system state in classical and quantum domains are reviewed. Shannon entropy and Rényi entropy are discussed. The notion of tomographic entropy determined by the probability distribution in the phase space of the classical system and by the density operator of the quantum system is considered. Inequalities for the tomographic entropies in classical and quantum domains are studied, and a difference in the form of these inequalities in corresponding domains is suggested as a test to clarify the classicality and quantumness of the system state in quantum optics experiments. A new bound for tomographic entropy (ln πe)Φ(θ) depending on the local oscillator phase difference in homodyne photon detection experiments is discussed.
Classical Trajectories and Quantum Spectra
NASA Technical Reports Server (NTRS)
Mielnik, Bogdan; Reyes, Marco A.
19960101
A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but nonperturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.
Unraveling Quantum Annealers using Classical Hardness.
MartinMayor, Victor; Hen, Itay
20150101
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as 'DWave' chips, promise to solve practical optimization problems potentially faster than conventional 'classical' computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spinglass theory that recognize 'temperature chaos' as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the DWave Two chip on different temperaturechaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip. PMID:26483257
Semenov, Alexander; Babikov, Dmitri
20140128
The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H{sub 2} and Na + N{sub 2}. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through tenorders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard fullquantum scattering theory.
NASA Astrophysics Data System (ADS)
Semenov, Alexander; Babikov, Dmitri
20140101
The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H2 and Na + N2. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through tenorders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard fullquantum scattering theory.
Decoherence, chaos, the quantum and the classical
Zurek, W.H.; Paz, J.P.
19940401
The key ideas of the environmentinduced decoherence approach are reviewed. Application of decoherence to the transition from quantum to classical in open quantum systems with chaotic classical analogs is described. The arrow of time is, in this context, a result of the information loss to the correlations with the environment. The asymptotic rate of entropy production (which is reached quickly, on the dynamical timescale) is independent of the details of the coupling of the quantum system to the environment, and is set by the Lyapunov exponents. We also briefly outline the existential interpretation of quantum mechanics, justifying the slogan ``No information without representation.``
Thermodynamic integration from classical to quantum mechanics
Habershon, Scott; Manolopoulos, David E.
20111214
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a wellestablished method with an analysis of a onedimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
Decoherence, chaos, the quantum and the classical
NASA Astrophysics Data System (ADS)
Zurek, W. H.; Paz, J. P.
The key ideas of the environmentinduced decoherence approach are reviewed. Application of decoherence to the transition from quantum to classical in open quantum systems with chaotic classical analogs is described. The arrow of time is, in this context, a result of the information loss to the correlations with the environment. The asymptotic rate of entropy production (which is reached quickly, on the dynamical timescale) is independent of the details of the coupling of the quantum system to the environment, and is set by the Lyapunov exponents. We also briefly outline the existential interpretation of quantum mechanics, justifying the slogan, no information without representation.
Quantum and Classical Electrostatics Among Atoms
NASA Astrophysics Data System (ADS)
Doerr, T. P.; Obolensky, O. I.; Ogurtsov, A. Y.; Yu, YiKuo
Quantum theory has been unquestionably successful at describing physics at the atomic scale. However, it becomes more difficult to apply as the system size grows. On the other hand, classical physics breaks down at sufficiently short length scales but is clearly correct at larger distances. The purpose of methods such as QM/MM is to gain the advantages of both quantum and classical regimes: quantum theory should provide accuracy at the shortest scales, and classical theory, with its somewhat more tractable computational demands, allows results to be computed for systems that would be inaccessible with a purely quantum approach. This strategy will be most effective when one knows with good accuracy the length scale at which quantum calculations are no longer necessary and classical calculations are sufficient. To this end, we have performed both classical and quantum calculations for systems comprising a small number of atoms for which experimental data is also available. The classical calculations are fully exact; the quantum calculations are at the MP4(SDTQ)/augccpV5Z and CCSD(T)/augccpV5Z levels. The precision of both sets of calculations along with the existence of experimental results allows us to draw conclusions about the range of utility of the respective calculations. This research was supported by the Intramural Research Program of the NIH, NLM and utilized the computational resources of the NIH HPC Biowulf cluster.
Martinez, Franz; Hanna, Gabriel
20160519
In a previous study (Martinez, F.; Hanna, G. Chem. Phys. Lett. 2013, 573, 7783), we demonstrated the ability of two approximate solutions of the quantumclassical Liouville equation (QCLE) for qualitatively capturing the electronic dynamics in the pumpprobe transient absorption (TA) signal of a model of a condensed phase photoinduced electron transfer reaction whose ground and excited donor states have the same equilibrium geometry. However, the question remained as to the ability of these solutions to treat the more complex situation in which the electronic states are coupled to a lowfrequency innersphere harmonic vibrational mode (representing an intramolecular mode of the donoracceptor complex) that shifts their equilibrium geometries with respect to each other and thereby gives rise to signatures of vibrational dynamics in the TA signal. Thus, in this study, we investigated this situation by treating the vibrational mode both quantum mechanically and classically within the context of the approximate Poisson bracket mapping equation (PBME) and forwardbackward trajectory solutions (FBTS) of the QCLE. Depending on the definition of the quantum subsystem, both PBME and FBTS are capable of qualitatively capturing several of the main features in the exact TA signal and quantitatively capturing the characteristic time scale of the vibrational dynamics, despite the moderately strong subsystembath coupling in this model. Particularly, we found that treating the vibrational mode quantum mechanically using either PBME or FBTS better captures the signatures of the vibrational dynamics, while treating it classically using FBTS better captures the decay in the signal. These findings underscore the utility of the PBME and FBTS approaches for efficiently modeling and interpreting TA signals. PMID:26766568
Unraveling Quantum Annealers using Classical Hardness
MartinMayor, Victor; Hen, Itay
20150101
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘DWave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spinglass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the DWave Two chip on different temperaturechaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip. PMID:26483257
Understanding singularities — Classical and quantum
NASA Astrophysics Data System (ADS)
Konkowski, Deborah A.; Helliwell, Thomas M.
20160101
The definitions of classical and quantum singularities are reviewed. Examples are given of both as well as their utility in general relativity. In particular, the classical and quantum singularity structure of certain interesting conformally static spherically symmetric spacetimes modeling scalar field collapse are reviewed. The spacetimes include the Roberts spacetime, the HusainMartinezNuñez spacetime and the Fonarev spacetime. The importance of understanding spacetime singularity structure is discussed.
Quantum dynamics simulation with classical oscillators
NASA Astrophysics Data System (ADS)
Briggs, John S.; Eisfeld, Alexander
20131201
In a previous paper [J. S. Briggs and A. Eisfeld, Phys. Rev. APLRAAN1050294710.1103/PhysRevA.85.052111 85, 052111 (2012)] we showed that the time development of the complex amplitudes of N coupled quantum states can be mapped by the time development of positions and velocities of N coupled classical oscillators. Here we examine to what extent this mapping can be realized to simulate the “quantum,” properties of entanglement and qubit manipulation. By working through specific examples, e.g., of quantum gate operation, we seek to illuminate quantum and classical differences which hitherto have been treated more mathematically. In addition, we show that important quantum coupled phenomena, such as the LandauZener transition and the occurrence of Fano resonances can be simulated by classical oscillators.
Quantum Backreaction on Classical'' Variables
Anderson, A. Blackett Laboratory, Imperial College, Prince Consort Rd., London SW7 2BZ )
19950130
A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled HamiltonHeisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become entangled with the quantum variables with the result that the value of the quasiclassical variables depends on the quantum state. This provides a formalism to compute the backreaction of any quantum system on a quasiclassical one. In particular, it leads to a natural candidate for a theory of gravity coupled to quantized matter in which the gravitational field is not quantized.
Quantum phase uncertainties in the classical limit
NASA Technical Reports Server (NTRS)
Franson, James D.
19940101
Several sources of phase noise, including spontaneous emission noise and the loss of coherence due to whichpath information, are examined in the classical limit of high field intensities. Although the origin of these effects may appear to be quantummechanical in nature, it is found that classical analogies for these effects exist in the form of chaos.
Classical and QuantumMechanical State Reconstruction
ERIC Educational Resources Information Center
Khanna, F. C.; Mello, P. A.; Revzen, M.
20120101
The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…
Classical underpinnings of gravitationally induced quantum interference
Mannheim, P.D.
19980201
We show that the gravitational modification of the phase of a neutron beam [the ColellaOverhauserWerner (COW) experiment] has a classical origin, being due to the time delay that classical particles experience in traversing a background gravitational field. Similarly, we show that classical light waves also undergo a phase shift in traversing a gravitational field. We show that the COW experiment respects the equivalence principle even in the presence of quantum mechanics. {copyright} {ital 1998} {ital The American Physical Society}
MultipleAccess QuantumClassical Networks
NASA Astrophysics Data System (ADS)
Razavi, Mohsen
20111001
A multiuser network that supports both classical and quantum communication is proposed. By relying on optical codedivision multiple access techniques, this system offers simultaneous key exchange between multiple pairs of network users. A lower bound on the secure key generation rate will be derived for decoystate quantum key distribution protocols.
Classical and quantum correlations under decoherence
Maziero, J.; Celeri, L. C.; Serra, R. M.; Vedral, V.
20091015
Recently some authors have pointed out that there exist nonclassical correlations which are more general, and possibly more fundamental, than entanglement. For these general quantum correlations and their classical counterparts, under the action of decoherence, we identify three general types of dynamics that include a peculiar sudden change in their decay rates. We show that, under suitable conditions, the classical correlation is unaffected by decoherence. Such dynamic behavior suggests an operational measure of both classical and quantum correlations that can be computed without any extremization procedur000.
Classical noise, quantum noise and secure communication
NASA Astrophysics Data System (ADS)
Tannous, C.; Langlois, J.
20160101
Secure communication based on message encryption might be performed by combining the message with controlled noise (called pseudonoise) as performed in spreadspectrum communication used presently in WiFi and smartphone telecommunication systems. Quantum communication based on entanglement is another route for securing communications as demonstrated by several important experiments described in this work. The central role played by the photon in unifying the description of classical and quantum noise as major ingredients of secure communication systems is highlighted and described on the basis of the classical and quantum fluctuation dissipation theorems.
Classical and quantum correlative capacities of quantum systems
Li Nan; Luo Shunlong
20111015
How strongly can one system be correlated with another? In the classical world, this basic question concerning correlative capacity has a very satisfying answer: The ''effective size'' of the marginal system, as quantified by the Shannon entropy, sets a tight upper bound to the correlations, as quantified by the mutual information. Although in the quantum world bipartite correlations, like their classical counterparts, are also well quantified by mutual information, the similarity ends here: The correlations in a bipartite quantum system can be twice as large as the marginal entropy. In the paradigm of quantum discord, the correlations are split into classical and quantum components, and it was conjectured that both the classical and quantum correlations are (like the classical mutual information) bounded above by each subsystem's entropy. In this work, by exploiting the interplay between entanglement of formation, mutual information, and quantum discord, we disprove that conjecture. We further indicate a scheme to restore harmony between quantum and classical correlative capacities. The results illustrate dramatically the asymmetric nature of quantum discord and highlight some subtle and unusual features of quantum correlations.
NUCLEAR MIXING METERS FOR CLASSICAL NOVAE
Kelly, Keegan J.; Iliadis, Christian; Downen, Lori; Champagne, Art; José, Jordi
20131110
Classical novae are caused by mass transfer episodes from a mainsequence star onto a white dwarf via Roche lobe overflow. This material possesses angular momentum and forms an accretion disk around the white dwarf. Ultimately, a fraction of this material spirals in and piles up on the white dwarf surface under electrondegenerate conditions. The subsequently occurring thermonuclear runaway reaches hundreds of megakelvin and explosively ejects matter into the interstellar medium. The exact peak temperature strongly depends on the underlying white dwarf mass, the accreted mass and metallicity, and the initial white dwarf luminosity. Observations of elemental abundance enrichments in these classical nova events imply that the ejected matter consists not only of processed solar material from the mainsequence partner but also of material from the outer layers of the underlying white dwarf. This indicates that white dwarf and accreted matter mix prior to the thermonuclear runaway. The processes by which this mixing occurs require further investigation to be understood. In this work, we analyze elemental abundances ejected from hydrodynamic nova models in search of elemental abundance ratios that are useful indicators of the total amount of mixing. We identify the abundance ratios ΣCNO/H, Ne/H, Mg/H, Al/H, and Si/H as useful mixing meters in ONe novae. The impact of thermonuclear reaction rate uncertainties on the mixing meters is investigated using Monte Carlo postprocessing network calculations with temperaturedensity evolutions of all mass zones computed by the hydrodynamic models. We find that the current uncertainties in the {sup 30}P(p, γ){sup 31}S rate influence the Si/H abundance ratio, but overall the mixing meters found here are robust against nuclear physics uncertainties. A comparison of our results with observations of ONe novae provides strong constraints for classical nova models.
Entanglement in the classical limit: Quantum correlations from classical probabilities
Matzkin, A.
20110815
We investigate entanglement for a composite closed system endowed with a scaling property which allows the dynamics to be kept invariant while the effective Planck constant ({Dirac_h}/2{pi}){sub eff} of the system is varied. Entanglement increases as ({Dirac_h}/2{pi}){sub eff}{yields}0. Moreover, for sufficiently low ({Dirac_h}/2{pi}){sub eff} the evolution of the quantum correlations, encapsulated, for example, in the quantum discord, can be obtained from the mutual information of the corresponding classical system. We show this behavior is due to the local suppression of path interferences in the interaction that generates the entanglement.
Quantum and classical phases in optomechanics
NASA Astrophysics Data System (ADS)
Armata, Federico; Latmiral, Ludovico; Pikovski, Igor; Vanner, Michael R.; Brukner, Časlav; Kim, M. S.
20160601
The control of quantum systems requires the ability to change and readout the phase of a system. The noncommutativity of canonical conjugate operators can induce phases on quantum systems, which can be employed for implementing phase gates and for precision measurements. Here we study the phase acquired by a radiation field after its radiation pressure interaction with a mechanical oscillator, and compare the classical and quantum contributions. The classical description can reproduce the nonlinearity induced by the mechanical oscillator and the loss of correlations between mechanics and optical field at certain interaction times. Such features alone are therefore insufficient for probing the quantum nature of the interaction. Our results thus isolate genuine quantum contributions of the optomechanical interaction that could be probed in current experiments.
Trading Classical and Quantum Computational Resources
NASA Astrophysics Data System (ADS)
Bravyi, Sergey; Smith, Graeme; Smolin, John A.
20160401
We propose examples of a hybrid quantumclassical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First, we consider sparse quantum circuits such that each qubit participates in O (1 ) twoqubit gates. It is shown that any sparse circuit on n +k qubits can be simulated by sparse circuits on n qubits and a classical processing that takes time 2O (k )poly (n ) . Second, we study Paulibased computation (PBC), where allowed operations are nondestructive eigenvalue measurements of n qubit Pauli operators. The computation begins by initializing each qubit in the socalled magic state. This model is known to be equivalent to the universal quantum computer. We show that any PBC on n +k qubits can be simulated by PBCs on n qubits and a classical processing that takes time 2O (k )poly (n ). Finally, we propose a purely classical algorithm that can simulate a PBC on n qubits in a time 2α npoly (n ) , where α ≈0.94 . This improves upon the bruteforce simulation method, which takes time 2npoly (n ). Our algorithm exploits the fact that n fold tensor products of magic states admit a lowrank decomposition into n qubit stabilizer states.
Quantumclassical crossover in electrodynamics
Polonyi, Janos
20060915
A classical field theory is proposed for the electric current and the electromagnetic field interpolating between microscopic and macroscopic domains. It represents a generalization of the density functional for the dynamics of the current and the electromagnetic field in the quantum side of the crossover and reproduces standard classical electrodynamics on the other side. The effective action derived in the closed time path formalism and the equations of motion follow from the variational principle. The polarization of the Diracsea can be taken into account in the quadratic approximation of the action by the introduction of the deplacement field strengths as in conventional classical electrodynamics. Decoherence appears naturally as a simple oneloop effect in this formalism. It is argued that the radiation time arrow is generated from the quantum boundary conditions in time by decoherence at the quantumclassical crossover and the AbrahamLorentz force arises from the accelerating charge or from other charges in the macroscopic or the microscopic side, respectively. The functional form of the quantum renormalization group, the generalization of the renormalization group method for the density matrix, is proposed to follow the scale dependence through the quantumclassical crossover in a systematical manner.
Entanglement in QuantumClassical Hybrid
NASA Technical Reports Server (NTRS)
Zak, Michail
20110101
It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, nonclassical systems such as quantumclassical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantuminspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the HamiltonJacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Nonlocality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of nonlocality in physics.
Large classical universes emerging from quantum cosmology
PintoNeto, Nelson
20090415
It is generally believed that one cannot obtain a large universe from quantum cosmological models without an inflationary phase in the classical expanding era because the typical size of the universe after leaving the quantum regime should be around the Planck length, and the standard decelerated classical expansion after that is not sufficient to enlarge the universe in the time available. For instance, in many quantum minisuperspace bouncing models studied in the literature, solutions where the universe leaves the quantum regime in the expanding phase with appropriate size have negligible probability amplitude with respect to solutions leaving this regime around the Planck length. In this paper, I present a general class of moving Gaussian solutions of the WheelerDeWitt equation where the velocity of the wave in minisuperspace along the scale factor axis, which is the new large parameter introduced in order to circumvent the abovementioned problem, induces a large acceleration around the quantum bounce, forcing the universe to leave the quantum regime sufficiently big to increase afterwards to the present size, without needing any classical inflationary phase in between, and with reasonable relative probability amplitudes with respect to models leaving the quantum regime around the Planck scale. Furthermore, linear perturbations around this background model are free of any transPlanckian problem.
Classical versus quantum errors in quantum computation of dynamical systems.
Rossini, Davide; Benenti, Giuliano; Casati, Giulio
20041101
We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum motion when the system's parameters are perturbed or when there are unitary errors in the quantum gates implementing the quantum algorithm. While the first kind of errors has a classical limit, the second one has no classical analog. It is shown that, whereas in the first case ("classical errors") the decay of fidelity is very sensitive to the dynamical regime, in the second case ("quantum errors") it is almost independent of the dynamical behavior of the simulated system. Therefore, the rich variety of behaviors found in the study of the stability of quantum motion under "classical" perturbations has no correspondence in the fidelity of quantum computation under its natural perturbations. In particular, in this latter case it is not possible to recover the semiclassical regime in which the fidelity decays with a rate given by the classical Lyapunov exponent. PMID:15600737
Correspondence between quantum and classical information: Generalized quantum measurements
Grishanin, Boris A.; Zadkov, Victor N.
20060415
The concept of generalized quantum measurement is introduced as a transformation that sets a onetoone correspondence between the initial states of the measured object system and final states of the objectmeter system with the help of a classical informational index, unambiguously linked to a classically compatible set of quantum states. It is shown that the generalized quantum measurement concept covers all key types of quantum measurementstandard projective, entangling, fuzzy, and generalized measurements with a partial or complete destruction of initial information associated with the object. A special class of soft quantum measurements as a basic model for the fuzzy measurements widespread in physics is introduced and its information properties are studied in detail. Also, a special class of partially destructive measurements mapping all states of the Hilbert space of a finitedimensional quantum system onto the basis states of an infinitedimensional quantum system is considered.
Crossover from quantum to classical transport
NASA Astrophysics Data System (ADS)
Morr, Dirk K.
20160101
Understanding the crossover from quantum to classical transport has become of fundamental importance not only for technological applications due to the creation of sub10nm transistors  an important building block of our modern life  but also for elucidating the role played by quantum mechanics in the evolutionary fitness of biological complexes. This article provides a basic introduction into the nature of charge and energy transport in the quantum and classical regimes. It discusses the characteristic transport properties in both limits and demonstrates how they can be connected through the loss of quantum mechanical coherence. The salient features of the crossover physics are identified, and their importance in opening new transport regimes and in understanding efficient and robust energy transport in biological complexes are demonstrated.
Classical and quantum routes to linear magnetoresistance.
Hu, Jingshi; Rosenbaum, T F
20080901
The hallmark of materials science is the ability to tailor the microstructure of a given material to provide a desired response. Carbon mixed with iron provides the steel of buildings and bridges; impurities sprinkled in silicon single crystals form the raw materials of the electronics revolution; pinning centres in superconductors let them become powerful magnets. Here, we show that either adding a few parts per million of the proper chemical impurities to indium antimonide, a wellknown semiconductor, or redesigning the material's structure on the micrometre scale, can transform its response to an applied magnetic field. The former approach is purely quantum mechanical; the latter a classical outgrowth of disorder, turned to advantage. In both cases, the magnetoresistive responseat the heart of magnetic sensor technologycan be converted to a simple, large and linear function of field that does not saturate. Harnessing the effects of disorder has the further advantage of extending the useful applications range of such a magnetic sensor to very high temperatures by circumventing the usual limitations imposed by phonon scattering. PMID:18719705
Quantum Correlations in MixedState Metrology
NASA Astrophysics Data System (ADS)
Modi, Kavan; Cable, Hugo; Williamson, Mark; Vedral, Vlatko
20111001
We analyze the effects of quantum correlations, such as entanglement and discord, on the efficiency of phase estimation by studying four quantum circuits that can be readily implemented using NMR techniques. These circuits define a standard strategy of repeated singlequbit measurements, a classical strategy where only classical correlations are allowed, and two quantum strategies where nonclassical correlations are allowed. In addition to counting space (number of qubits) and time (number of gates) requirements, we introduce mixedness as a key constraint of the experiment. We compare the efficiency of the four strategies as a function of the mixedness parameter. We find that the quantum strategy gives N enhancement over the standard strategy for the same amount of mixedness. This result applies even for highly mixed states that have nonclassical correlations but no entanglement.
Applying classical geometry intuition to quantum spin
NASA Astrophysics Data System (ADS)
Durfee, Dallin S.; Archibald, James L.
20160901
Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin1/2 system. Rather than a mathematically rigorous derivation, the relationships are found by forcing expectation values of the different basis states to have the properties we expect of a classical, geometric coordinate system. The process highlights the correspondence of quantum angular momentum with classical notions of geometric orthogonality, even for the inherently nonclassical spin1/2 system. In the process, differences in and connections between geometrical space and Hilbert space are illustrated.
Classical Simulated Annealing Using Quantum Analogues
NASA Astrophysics Data System (ADS)
La Cour, Brian R.; Troupe, James E.; Mark, Hans M.
20160801
In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of multiple simultaneous spin flips at each annealing step as an analogue to quantum spin coherence as well as modifications of the Boltzmann acceptance probability to mimic quantum tunneling. We find that the use of multiple spin flips can indeed be advantageous under certain annealing schedules, but only for long anneal times.
Classical Simulated Annealing Using Quantum Analogues
NASA Astrophysics Data System (ADS)
La Cour, Brian R.; Troupe, James E.; Mark, Hans M.
20160601
In this paper we consider the use of certain classical analogues to quantum tunneling behavior to improve the performance of simulated annealing on a discrete spin system of the general Ising form. Specifically, we consider the use of multiple simultaneous spin flips at each annealing step as an analogue to quantum spin coherence as well as modifications of the Boltzmann acceptance probability to mimic quantum tunneling. We find that the use of multiple spin flips can indeed be advantageous under certain annealing schedules, but only for long anneal times.
Comparison of Classical and Quantum Mechanical Uncertainties.
ERIC Educational Resources Information Center
Peslak, John, Jr.
19790101
Comparisons are made for the particleinabox, the harmonic oscillator, and the oneelectron atom. A classical uncertainty principle is derived and compared with its quantummechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
Classical and quantum Kummer shape algebras
NASA Astrophysics Data System (ADS)
Odzijewicz, A.; Wawreniuk, E.
20160701
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.
Quantum and classical optics–emerging links
NASA Astrophysics Data System (ADS)
Eberly, J. H.; Qian, XiaoFeng; Qasimi, Asma Al; Ali, Hazrat; Alonso, M. A.; GutiérrezCuevas, R.; Little, Bethany J.; Howell, John C.; Malhotra, Tanya; Vamivakas, A. N.
20160601
Quantum optics and classical optics are linked in ways that are becoming apparent as a result of numerous recent detailed examinations of the relationships that elementary notions of optics have with each other. These elementary notions include interference, polarization, coherence, complementarity and entanglement. All of them are present in both quantum and classical optics. They have historic origins, and at least partly for this reason not all of them have quantitative definitions that are universally accepted. This makes further investigation into their engagement in optics very desirable. We pay particular attention to effects that arise from the mere coexistence of separately identifiable and readily available vector spaces. Exploitation of these vectorspace relationships are shown to have unfamiliar theoretical implications and new options for observation. It is our goal to bring emerging quantum–classical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.
Quantumtoclassical crossover near quantum critical point
Vasin, M.; Ryzhov, V.; Vinokur, V. M.
20151221
A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while nondissipative quantum dynamics is described in detail, the question, that is not thoroughly understood is how the omnipresent dissipative processes enter the critical dynamics near a quantum critical point (QCP). Here we report a general approach enabling inclusion of both adiabatic and dissipative processes into the critical dynamics on the same footing. We reveal three distinct critical modes, the adiabatic quantum mode (AQM), the dissipative classical mode [classical critical dynamics mode (CCDM)], and the dissipative quantum critical mode (DQCM). We find that as a result of the transitionmore » from the regime dominated by thermal fluctuations to that governed by the quantum ones, the system acquires effective dimension d+zΛ(T), where z is the dynamical exponent, and temperaturedepending parameter Λ(T)ε[0, 1] decreases with the temperature such that Λ(T=0) = 1 and Λ(T →∞) = 0. Lastly, our findings lead to a unified picture of quantum critical phenomena including both dissipation and dissipationless quantum dynamic effects and offer a quantitative description of the quantumtoclassical crossover.« less
Quantumtoclassical crossover near quantum critical point
NASA Astrophysics Data System (ADS)
Vasin, M.; Ryzhov, V.; Vinokur, V. M.
20151201
A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while nondissipative quantum dynamics is described in detail, the question, that is not thoroughly understood is how the omnipresent dissipative processes enter the critical dynamics near a quantum critical point (QCP). Here we report a general approach enabling inclusion of both adiabatic and dissipative processes into the critical dynamics on the same footing. We reveal three distinct critical modes, the adiabatic quantum mode (AQM), the dissipative classical mode [classical critical dynamics mode (CCDM)], and the dissipative quantum critical mode (DQCM). We find that as a result of the transition from the regime dominated by thermal fluctuations to that governed by the quantum ones, the system acquires effective dimension d + zΛ(T), where z is the dynamical exponent, and temperaturedepending parameter Λ(T) ∈ [0, 1] decreases with the temperature such that Λ(T = 0) = 1 and Λ(T → ∞) = 0. Our findings lead to a unified picture of quantum critical phenomena including both dissipation and dissipationless quantum dynamic effects and offer a quantitative description of the quantumtoclassical crossover.
Quantumtoclassical crossover near quantum critical point
Vasin, M.; Ryzhov, V.; Vinokur, V. M.
20150101
A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while nondissipative quantum dynamics is described in detail, the question, that is not thoroughly understood is how the omnipresent dissipative processes enter the critical dynamics near a quantum critical point (QCP). Here we report a general approach enabling inclusion of both adiabatic and dissipative processes into the critical dynamics on the same footing. We reveal three distinct critical modes, the adiabatic quantum mode (AQM), the dissipative classical mode [classical critical dynamics mode (CCDM)], and the dissipative quantum critical mode (DQCM). We find that as a result of the transition from the regime dominated by thermal fluctuations to that governed by the quantum ones, the system acquires effective dimension d + zΛ(T), where z is the dynamical exponent, and temperaturedepending parameter Λ(T) ∈ [0, 1] decreases with the temperature such that Λ(T = 0) = 1 and Λ(T → ∞) = 0. Our findings lead to a unified picture of quantum critical phenomena including both dissipation and dissipationless quantum dynamic effects and offer a quantitative description of the quantumtoclassical crossover. PMID:26688102
Quantumtoclassical crossover near quantum critical point
Vasin, M.; Ryzhov, V.; Vinokur, V. M.
20151221
A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while nondissipative quantum dynamics is described in detail, the question, that is not thoroughly understood is how the omnipresent dissipative processes enter the critical dynamics near a quantum critical point (QCP). Here we report a general approach enabling inclusion of both adiabatic and dissipative processes into the critical dynamics on the same footing. We reveal three distinct critical modes, the adiabatic quantum mode (AQM), the dissipative classical mode [classical critical dynamics mode (CCDM)], and the dissipative quantum critical mode (DQCM). We find that as a result of the transition from the regime dominated by thermal fluctuations to that governed by the quantum ones, the system acquires effective dimension d+zΛ(T), where z is the dynamical exponent, and temperaturedepending parameter Λ(T)ε[0, 1] decreases with the temperature such that Λ(T=0) = 1 and Λ(T →∞) = 0. Lastly, our findings lead to a unified picture of quantum critical phenomena including both dissipation and dissipationless quantum dynamic effects and offer a quantitative description of the quantumtoclassical crossover.
Experimental tests of classical and quantum dimensionality.
Ahrens, Johan; Badziąg, Piotr; Pawłowski, Marcin; Zukowski, Marek; Bourennane, Mohamed
20140411
We report on an experimental test of classical and quantum dimension. We have used a dimension witness that can distinguish between quantum and classical systems of dimensions two, three, and four and performed the experiment for all five cases. The witness we have chosen is a base of semideviceindependent cryptographic and randomness expansion protocols. Therefore, the part of the experiment in which qubits were used is a realization of these protocols. In our work we also present an analytic method for finding the maximum quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness. PMID:24765923
Kojima, H; Yamada, A; Okazaki, S
20150501
The intramolecular proton transfer reaction of malonaldehyde in neon solvent has been investigated by mixed quantumclassical molecular dynamics (QCMD) calculations and fully classical molecular dynamics (FCMD) calculations. Comparing these calculated results with those for malonaldehyde in water reported in Part I [A. Yamada, H. Kojima, and S. Okazaki, J. Chem. Phys. 141, 084509 (2014)], the solvent dependence of the reaction rate, the reaction mechanism involved, and the quantum effect therein have been investigated. With FCMD, the reaction rate in weakly interacting neon is lower than that in strongly interacting water. However, with QCMD, the order of the reaction rates is reversed. To investigate the mechanisms in detail, the reactions were categorized into three mechanisms: tunneling, thermal activation, and barrier vanishing. Then, the quantum and solvent effects were analyzed from the viewpoint of the reaction mechanism focusing on the shape of potential energy curve and its fluctuations. The higher reaction rate that was found for neon in QCMD compared with that found for water solvent arises from the tunneling reactions because of the nearly symmetric doublewell shape of the potential curve in neon. The thermal activation and barrier vanishing reactions were also accelerated by the zeropoint energy. The number of reactions based on these two mechanisms in water was greater than that in neon in both QCMD and FCMD because these reactions are dominated by the strength of solutesolvent interactions. PMID:25956108
NASA Astrophysics Data System (ADS)
Kojima, H.; Yamada, A.; Okazaki, S.
20150501
The intramolecular proton transfer reaction of malonaldehyde in neon solvent has been investigated by mixed quantumclassical molecular dynamics (QCMD) calculations and fully classical molecular dynamics (FCMD) calculations. Comparing these calculated results with those for malonaldehyde in water reported in Part I [A. Yamada, H. Kojima, and S. Okazaki, J. Chem. Phys. 141, 084509 (2014)], the solvent dependence of the reaction rate, the reaction mechanism involved, and the quantum effect therein have been investigated. With FCMD, the reaction rate in weakly interacting neon is lower than that in strongly interacting water. However, with QCMD, the order of the reaction rates is reversed. To investigate the mechanisms in detail, the reactions were categorized into three mechanisms: tunneling, thermal activation, and barrier vanishing. Then, the quantum and solvent effects were analyzed from the viewpoint of the reaction mechanism focusing on the shape of potential energy curve and its fluctuations. The higher reaction rate that was found for neon in QCMD compared with that found for water solvent arises from the tunneling reactions because of the nearly symmetric doublewell shape of the potential curve in neon. The thermal activation and barrier vanishing reactions were also accelerated by the zeropoint energy. The number of reactions based on these two mechanisms in water was greater than that in neon in both QCMD and FCMD because these reactions are dominated by the strength of solutesolvent interactions.
Monogamy properties of quantum and classical correlations
Giorgi, Gian Luca
20111115
In contrast with entanglement, as measured by concurrence, in general, quantum discord does not possess the property of monogamy; that is, there is no tradeoff between the quantum discord shared by a pair of subsystems and the quantum discord that both of them can share with a third party. Here, we show that, as far as monogamy is considered, quantum discord of pure states is equivalent to the entanglement of formation. This result allows one to analytically prove that none of the pure threequbit states belonging to the subclass of W states is monogamous. A suitable physical interpretation of the meaning of the correlation information as a quantifier of monogamy for the total information is also given. Finally, we prove that, for rank 2 twoqubit states, discord and classical correlations are bounded from above by singlequbit von Neumann entropies.
Classical codes in quantum state space
NASA Astrophysics Data System (ADS)
Howard, Mark
20151201
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between their corresponding strings. This allows a straightforward application of classical coding theory to find arrangements of operators or states with a given distance distribution. Using the simplex or extended ReedSolomon code in our construction recovers the discrete Wigner function, which has important applications in quantum information theory.
Monodisperse cluster crystals: Classical and quantum dynamics.
DíazMéndez, Rogelio; Mezzacapo, Fabio; Cinti, Fabio; Lechner, Wolfgang; Pupillo, Guido
20151101
We study the phases and dynamics of a gas of monodisperse particles interacting via softcore potentials in two spatial dimensions, which is of interest for softmatter colloidal systems and quantum atomic gases. Using exact theoretical methods, we demonstrate that the equilibrium lowtemperature classical phase simultaneously breaks continuous translational symmetry and dynamic spacetime homogeneity, whose absence is usually associated with outofequilibrium glassy phenomena. This results in an exotic selfassembled cluster crystal with coexisting liquidlike longtime dynamical properties, which corresponds to a classical analog of supersolid behavior. We demonstrate that the effects of quantum fluctuations and bosonic statistics on clusterglassy crystals are separate and competing: Zeropoint motion tends to destabilize crystalline order, which can be restored by bosonic statistics. PMID:26651695
Quantum and classical dissipation of charged particles
IbarraSierra, V.G.; AnzaldoMeneses, A.; Cardoso, J.L.; HernándezSaldaña, H.; Kunold, A.; RoaNeri, J.A.E.
20130815
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail.  Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle. •Classical and quantum dynamics of a damped electric charge.
Mesoscopic systems: classical irreversibility and quantum coherence.
Barbara, Bernard
20120928
Mesoscopic physics is a subdiscipline of condensedmatter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with largespin magnetic molecules called singlemolecule magnets (SMMs) with archetype Mn(12)ac. In general, the mesoscopic scale can be relatively large (e.g. micrometresized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the LandauZener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V(15), the leading decoherence terms of superconducting qubits seem to be associated with a nonMarkovian channel in which shortliving entanglements with distributions of twolevel systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)like
Time in classical and in quantum mechanics
NASA Astrophysics Data System (ADS)
Elçi, A.
20100701
This paper presents an analysis of the time concept in classical mechanics from the perspective of the invariants of a motion. The analysis shows that there is a conceptual gap concerning time in the DiracHeisenbergvon Neumann formalism and that Bohr's complementarity principle does not fill the gap. In the DiracHeisenbergvon Neumann formalism, a particle's properties are represented by Heisenberg matrices. This axiom is the source of the time problem in quantum mechanics.
New variables for classical and quantum gravity
NASA Technical Reports Server (NTRS)
Ashtekar, Abhay
19860101
A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced. These variables simplify the constraints of general relativity considerably and enable one to imbed the constraint surface in the phase space of Einstein's theory into that of YangMills theory. The imbedding suggests new ways of attacking a number of problems in both classical and quantum gravity. Some illustrative applications are discussed.
Quantum particles from coarse grained classical probabilities in phase space
Wetterich, C.
20100715
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.
Quantum uncertainty of mixed states based on skew information
Luo Shunlong
20060215
The uncertainty of a mixed state has two quite different origins: classical mixing and quantum randomness. While the classical aspect (mixedness) is significantly quantified by the von Neumann entropy, it seems that we still do not have a well accepted measure of quantum uncertainty. In terms of the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurements, we will propose an intrinsic measure for synthesizing quantum uncertainty of a mixed state and investigate its fundamental properties. We illustrate how it arises naturally from a naive hiddenvariable approach to entanglement and how it exhibits a simple relation to the notion of negativity, which is an entanglement monotone introduced quite recently. We further show that it has a dramatic nonextensive feature resembling the probability law relating operations of two events. This measure of quantum uncertainty provides an alternative quantity complementary to the von Neumann entropy for studying mixedness and quantum correlations.
Sharing the Quantum State and the Classical Information Simultaneously
NASA Astrophysics Data System (ADS)
Qin, Huawang; Dai, Yuewei
20160401
An efficient quantum secret sharing scheme is proposed, in which the quantum state and the classical information can be shared simultaneously through only one distribution. The dealer uses the operations of quantumcontrollednot and Hadamard gate to encode the secret quantum state and classical information, and the participants use the singleparticle measurements to recover the original quantum state and classical information. Compared to the existing schemes, our scheme is more efficient when the quantum state and the classical information need to be shared simultaneously.
Sharing the Quantum State and the Classical Information Simultaneously
NASA Astrophysics Data System (ADS)
Qin, Huawang; Dai, Yuewei
20160801
An efficient quantum secret sharing scheme is proposed, in which the quantum state and the classical information can be shared simultaneously through only one distribution. The dealer uses the operations of quantumcontrollednot and Hadamard gate to encode the secret quantum state and classical information, and the participants use the singleparticle measurements to recover the original quantum state and classical information. Compared to the existing schemes, our scheme is more efficient when the quantum state and the classical information need to be shared simultaneously.
How quantum are classical spin ices?
NASA Astrophysics Data System (ADS)
Gingras, Michel J. P.; Rau, Jeffrey G.
The pyrochlore spin ice compounds Dy2TiO7 and Ho2Ti2O7 are well described by classical Ising models down to low temperatures. Given the empirical success of this description, the question of the importance of quantum effects in these materials has been mostly ignored. We argue that the common wisdom that the strictly Ising moments of noninteracting Dy3+ and Ho3+ ions imply Ising interactions is too naive and that a more complex argument is needed to explain the close agreement between the classical Ising model theory and experiments. By considering a microscopic picture of the interactions in rareearth oxides, we show that the highrank multipolar interactions needed to induce quantum effects in these two materials are generated only very weakly by superexchange. Using this framework, we formulate an estimate of the scale of quantum effects in Dy2Ti2O7 and Ho2Ti2O7, finding it to be well below experimentally relevant temperatures. Published as: PHYSICAL REVIEW B 92, 144417 (2015).
Quantum to classical transition in quantum field theory
NASA Astrophysics Data System (ADS)
Lombardo, Fernando C.
19981201
We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for selfinteracting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a selfinteracting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the longwavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalartensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the EinsteinLangevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.
Classical and Quantum Probability for Biologists  Introduction
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei.
20100101
The aim of this review (oriented to biologists looking for applications of QM) is to provide a detailed comparative analysis of classical (Kolmogorovian) and quantum (Diracvon Neumann) models. We will stress differences in the definition of conditional probability and as a consequence in the structures of matrices of transition probabilities, especially the condition of double stochasticity which arises naturally in QM. One of the most fundamental differences between two models is deformation of the classical formula of total probability (FTP) which plays an important role in statistics and decision making. An additional term appears in the QMversion of FTP  so called interference term. Finally, we discuss Bell's inequality and show that the common viewpoint that its violation induces either nonlocality or "death of realism" has not been completely justified. For us it is merely a sign of nonKolmogorovianity of probabilistic data collected in a few experiments with incompatible setups of measurement devices.
Quantum manifestations of classical nonlinear resonances
NASA Astrophysics Data System (ADS)
Wisniacki, Diego A.; Schlagheck, Peter
20151201
When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties
Quantum manifestations of classical nonlinear resonances.
Wisniacki, Diego A; Schlagheck, Peter
20151201
When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties. PMID:26764790
Classical Information Storage in an nLevel Quantum System
NASA Astrophysics Data System (ADS)
Frenkel, Péter E.; Weiner, Mihály
20151201
A game is played by a team of two—say Alice and Bob—in which the value of a random variable x is revealed to Alice only, who cannot freely communicate with Bob. Instead, she is given a quantum nlevel system, respectively a classical nstate system, which she can put in possession of Bob in any state she wishes. We evaluate how successfully they managed to store and recover the value of x by requiring Bob to specify a value z and giving a reward of value f ( x, z) to the team. We show that whatever the probability distribution of x and the reward function f are, when using a quantum nlevel system, the maximum expected reward obtainable with the best possible team strategy is equal to that obtainable with the use of a classical nstate system. The proof relies on mixed discriminants of positive matrices and—perhaps surprisingly—an application of the SupplyDemand Theorem for bipartite graphs. As a corollary, we get an infinite set of new, dimension dependent inequalities regarding positive operator valued measures and density operators on complex nspace. As a further corollary, we see that the greatest value, with respect to a given distribution of x, of the mutual information I ( x; z) that is obtainable using an nlevel quantum system equals the analogous maximum for a classical nstate system.
Exploring Classically Chaotic Potentials with a Matter Wave Quantum Probe
Gattobigio, G. L.; Couvert, A.; Georgeot, B.; GueryOdelin, D.
20111216
We study an experimental setup in which a quantum probe, provided by a quasimonomode guided atom laser, interacts with a static localized attractive potential whose characteristic parameters are tunable. In this system, classical mechanics predicts a transition from regular to chaotic behavior as a result of the coupling between the different degrees of freedom. Our experimental results display a clear signature of this transition. On the basis of extensive numerical simulations, we discuss the quantum versus classical physics predictions in this context. This system opens new possibilities for investigating quantum scattering, provides a new testing ground for classical and quantum chaos, and enables us to revisit the quantumclassical correspondence.
Li Zhenni; Jin Jiasen; Yu Changshui
20110115
We present schemes for a type of oneparameter bipartite quantum state to probe quantum entanglement, quantum discord, the classical correlation, and the quantum state based on cavity QED. It is shown that our detection does not influence all these measured quantities. We also discuss how the spontaneous emission introduced by our probe atom influences our detection.
Arbiter as the Third Man in Classical and Quantum Games
NASA Astrophysics Data System (ADS)
Pykacz, Jarosław; FraÇkiewicz, Piotr
20101201
We study the possible influence of a not necessarily sincere arbiter on the course of classical and quantum 2×2 games and we show that this influence in the quantum case is much bigger than in the classical case. Extreme sensitivity of quantum games on initial states of quantum objects used as carriers of information in a game shows that a quantum game, contrary to a classical game, is not defined by a payoff matrix alone but also by an initial state of objects used to play a game. Therefore, two quantum games that have the same payoff matrices but begin with different initial states should be considered as different games.
NASA Astrophysics Data System (ADS)
Semenov, Alexander; Dubernet, MarieLise; Babikov, Dmitri
20140901
The mixed quantum/classical theory (MQCT) for inelastic moleculeatom scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is extended to treat a general case of an asymmetrictoprotor molecule in the bodyfixed reference frame. This complements a similar theory formulated in the spacefixed referenceframe [M. Ivanov, M.L. Dubernet, and D. Babikov, J. Chem. Phys. 140, 134301 (2014)]. Here, the goal was to develop an approximate computationally affordable treatment of the rotationally inelastic scattering and apply it to H2O + He. We found that MQCT is somewhat less accurate at lower scattering energies. For example, below E = 1000 cm1 the typical errors in the values of inelastic scattering cross sections are on the order of 10%. However, at higher scattering energies MQCT method appears to be rather accurate. Thus, at scattering energies above 2000 cm1 the errors are consistently in the range of 1%2%, which is basically our convergence criterion with respect to the number of trajectories. At these conditions our MQCT method remains computationally affordable. We found that computational cost of the fullycoupled MQCT calculations scales as n2, where n is the number of channels. This is more favorable than the fullquantum inelastic scattering calculations that scale as n3. Our conclusion is that for complex systems (heavy collision partners with many internal states) and at higher scattering energies MQCT may offer significant computational advantages.
Quantumclassical equivalence and groundstate factorization
NASA Astrophysics Data System (ADS)
Abouie, Jahanfar; Sepehrinia, Reza
20160201
We have performed an analytical study of quantumclassical equivalence for quantum XYspin chains with arbitrary interactions to explore the classical counterpart of the factorizing magnetic fields that drive the system into a separable ground state. We demonstrate that the factorizing line in the parameter space of a quantum model is equivalent to the socalled natural boundary that emerges in mapping the quantum XYmodel onto the twodimensional classical Ising model. As a result, we show that the quantum systems with the nonfactorizable ground state could not be mapped onto the classical Ising model. Based on the presented correspondence we suggest a promising method for obtaining the factorizing field of quantum systems through the commutation of the quantum Hamiltonian and the transfer matrix of the classical model.
QuantumClassical Hybrid for Information Processing
NASA Technical Reports Server (NTRS)
Zak, Michail
20110101
Based upon quantuminspired entanglement in quantumclassical hybrids, a simple algorithm for instantaneous transmissions of nonintentional messages (chosen at random) to remote distances is proposed. The idea is to implement instantaneous transmission of conditional information on remote distances via a quantumclassical hybrid that preserves superposition of random solutions, while allowing one to measure its state variables using classical methods. Such a hybrid system reinforces the advantages, and minimizes the limitations, of both quantum and classical characteristics. Consider n observers, and assume that each of them gets a copy of the system and runs it separately. Although they run identical systems, the outcomes of even synchronized runs may be different because the solutions of these systems are random. However, the global constrain must be satisfied. Therefore, if the observer #1 (the sender) made a measurement of the acceleration v(sub 1) at t =T, then the receiver, by measuring the corresponding acceleration v(sub 1) at t =T, may get a wrong value because the accelerations are random, and only their ratios are deterministic. Obviously, the transmission of this knowledge is instantaneous as soon as the measurements have been performed. In addition to that, the distance between the observers is irrelevant because the xcoordinate does not enter the governing equations. However, the Shannon information transmitted is zero. None of the senders can control the outcomes of their measurements because they are random. The senders cannot transmit intentional messages. Nevertheless, based on the transmitted knowledge, they can coordinate their actions based on conditional information. If the observer #1 knows his own measurements, the measurements of the others can be fully determined. It is important to emphasize that the origin of entanglement of all the observers is the joint probability density that couples their actions. There is no centralized source
Coarsening Measurement References and the QuantumtoClassical Transition
NASA Astrophysics Data System (ADS)
Jeong, Hyunseok; Lim, Youngrong; Kim, M. S.
20140101
We investigate the role of inefficiency in quantum measurements in the quantumtoclassical transition, and consistently observe the quantumtoclassical transition by coarsening the references of the measurements (e.g., when and where to measure). Our result suggests that the definition of measurement precision in quantum theory should include the degree of the observer's ability to precisely control the measurement references.
Nonlinear quantum equations: Classical field theory
RegoMonteiro, M. A.; Nobre, F. D.
20131015
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the KleinGordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a qplane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and KleinGordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Classical Physics and the Bounds of Quantum Correlations.
Frustaglia, Diego; Baltanás, José P; VelázquezAhumada, María C; FernándezPrieto, Armando; Lujambio, Aintzane; Losada, Vicente; Freire, Manuel J; Cabello, Adán
20160624
A unifying principle explaining the numerical bounds of quantum correlations remains elusive, despite the efforts devoted to identifying it. Here, we show that these bounds are indeed not exclusive to quantum theory: for any abstract correlation scenario with compatible measurements, models based on classical waves produce probability distributions indistinguishable from those of quantum theory and, therefore, share the same bounds. We demonstrate this finding by implementing classical microwaves that propagate along metersize transmissionline circuits and reproduce the probabilities of three emblematic quantum experiments. Our results show that the "quantum" bounds would also occur in a classical universe without quanta. The implications of this observation are discussed. PMID:27391707
Classical Physics and the Bounds of Quantum Correlations
NASA Astrophysics Data System (ADS)
Frustaglia, Diego; Baltanás, José P.; VelázquezAhumada, María C.; FernándezPrieto, Armando; Lujambio, Aintzane; Losada, Vicente; Freire, Manuel J.; Cabello, Adán
20160601
A unifying principle explaining the numerical bounds of quantum correlations remains elusive, despite the efforts devoted to identifying it. Here, we show that these bounds are indeed not exclusive to quantum theory: for any abstract correlation scenario with compatible measurements, models based on classical waves produce probability distributions indistinguishable from those of quantum theory and, therefore, share the same bounds. We demonstrate this finding by implementing classical microwaves that propagate along metersize transmissionline circuits and reproduce the probabilities of three emblematic quantum experiments. Our results show that the "quantum" bounds would also occur in a classical universe without quanta. The implications of this observation are discussed.
Fate of classical solitons in onedimensional quantum systems.
Pustilnik, M.; Matveev, K. A.
20151123
We study onedimensional quantum systems near the classical limit described by the Kortewegde Vries (KdV) equation. The excitations near this limit are the wellknown solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classicaltoquantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the LiebLiniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum onedimensional systems with a welldefined classical limit described by the KdV equation.
Beyond quantumclassical analogies: high time for agreement?
NASA Astrophysics Data System (ADS)
Marrocco, Michele
Lately, many quantumclassical analogies have been investigated and published in many acknowledged journals. Such a surge of research on conceptual connections between quantum and classical physics forces us to ask whether the correspondence between the quantum and classical interpretation of the reality is deeper than the correspondence principle stated by Bohr. Here, after a short introduction to quantumclassical analogies from the recent literature, we try to examine the question from the perspective of a possible agreement between quantum and classical laws. A paradigmatic example is given in the striking equivalence between the classical Mie theory of electromagnetic scattering from spherical scatterers and the corresponding quantummechanical wave scattering analyzed in terms of partial waves. The key features that make the correspondence possible are examined and finally employed to deal with the fundamental blackbody problem that marks the initial separation between classical and quantum physics. The procedure allows us to recover the blackbody spectrum in classical terms and the proof is rich in consequences. Among them, the strong analogy between the quantum vacuum and its classical counterpart.
Quantum evaporation of flavormixed particles
NASA Astrophysics Data System (ADS)
Medvedev, Mikhail V.
20140301
Particles whose propagation (mass) and interaction (flavor) bases are misaligned are mixed, e.g., neutrinos, quarks, Kaons, etc. We show that interactions (elastic scattering) of individual masseigenstates can result in their interconversions. Most intriguing and counterintuitive implication of this process is a new process, which we refer to as the ``quantum evaporation.'' Consider a mixed particle trapped in a gravitational potential. If such a particle scatters off something (e.g., from another mixed particle) elastically from time to time, this particle (or both particles, respectively) can eventually escape to infinity with no extra energy supplied. That is as if a ``flavormixed satellite'' hauled along a bumpy road puts itself in space without a rocket, fuel, etc. Of course, the process at hand is entirely quantum and has no counterpart in classical mechanics. It also has nothing to do with tunneling or other known processes. We discuss some implications to the dark matter physics, cosmology and cosmic neutrino background. Supported by grant DOE grant DEFG0207ER54940 and NSF grant AST1209665.
INCLINATION MIXING IN THE CLASSICAL KUIPER BELT
Volk, Kathryn; Malhotra, Renu
20110720
We investigate the longterm evolution of the inclinations of the known classical and resonant Kuiper Belt objects (KBOs). This is partially motivated by the observed bimodal inclination distribution and by the putative physical differences between the low and highinclination populations. We find that some classical KBOs undergo large changes in inclination over gigayear timescales, which means that a current member of the lowinclination population may have been in the highinclination population in the past, and vice versa. The dynamical mechanisms responsible for the time variability of inclinations are predominantly distant encounters with Neptune and chaotic diffusion near the boundaries of mean motion resonances. We reassess the correlations between inclination and physical properties including inclination time variability. We find that the sizeinclination and colorinclination correlations are less statistically significant than previously reported (mostly due to the increased size of the data set since previous works with some contribution from inclination variability). The time variability of inclinations does not change the previous finding that binary classical KBOs have lower inclinations than nonbinary objects. Our study of resonant objects in the classical Kuiper Belt region includes objects in the 3:2, 7:4, 2:1, and eight higherorder mean motion resonances. We find that these objects (some of which were previously classified as nonresonant) undergo larger changes in inclination compared to the nonresonant population, indicating that their current inclinations are not generally representative of their original inclinations. They are also less stable on gigayear timescales.
Ergodicity and mixing in quantum dynamics.
Zhang, Dongliang; Quan, H T; Wu, Biao
20160801
After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with the usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy. PMID:27627289
Complementarity of quantum discord and classically accessible information
Zwolak, Michael P.; Zurek, Wojciech H.
20130520
The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observableindependent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasiclassical pointer observable. Other observables are accessible only via correlations with the pointer observable. In addition, we prove an antisymmetry property relating accessible information and discord. Itmore » shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. Lastly, the resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.« less
Complementarity of quantum discord and classically accessible information
Zwolak, Michael P.; Zurek, Wojciech H.
20130520
The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observableindependent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasiclassical pointer observable. Other observables are accessible only via correlations with the pointer observable. In addition, we prove an antisymmetry property relating accessible information and discord. It shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. Lastly, the resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.
Extracting classical correlations from a bipartite quantum system
Hamieh, S.; Qi, J.; Siminovitch, D.; Ali, M.K.
20030101
In this paper, we discuss the problem of splitting of the total correlations for a bipartite quantum state described by the Von Neumann mutual information into classical and quantum parts. We propose a measure of the classical correlations as the difference between the Von Neumann mutual information and the relative entropy of entanglement. We compare this measure with different measures proposed in the literature.
Classical and thermodynamic limits for generalised quantum spin systems
NASA Astrophysics Data System (ADS)
Duffield, N. G.
19900101
We prove that the rescaled upper and lower symbols for arbitrary generalised quantum spin systems converge in the classical limit. For a large class of models this enables us to derive the asyptotics of quantum free energies in the classical and in the thermodynamic limit.
Semenov, Alexander; Dubernet, MarieLise; Babikov, Dmitri
20140921
The mixed quantum/classical theory (MQCT) for inelastic moleculeatom scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is extended to treat a general case of an asymmetrictoprotor molecule in the bodyfixed reference frame. This complements a similar theory formulated in the spacefixed referenceframe [M. Ivanov, M.L. Dubernet, and D. Babikov, J. Chem. Phys. 140, 134301 (2014)]. Here, the goal was to develop an approximate computationally affordable treatment of the rotationally inelastic scattering and apply it to H{sub 2}O + He. We found that MQCT is somewhat less accurate at lower scattering energies. For example, below E = 1000 cm{sup −1} the typical errors in the values of inelastic scattering cross sections are on the order of 10%. However, at higher scattering energies MQCT method appears to be rather accurate. Thus, at scattering energies above 2000 cm{sup −1} the errors are consistently in the range of 1%–2%, which is basically our convergence criterion with respect to the number of trajectories. At these conditions our MQCT method remains computationally affordable. We found that computational cost of the fullycoupled MQCT calculations scales as n{sup 2}, where n is the number of channels. This is more favorable than the fullquantum inelastic scattering calculations that scale as n{sup 3}. Our conclusion is that for complex systems (heavy collision partners with many internal states) and at higher scattering energies MQCT may offer significant computational advantages.
Heterotic quantum and classical computing on convergence spaces
NASA Astrophysics Data System (ADS)
Patten, D. R.; Jakel, D. W.; Irwin, R. J.; Blair, H. A.
20150501
Categorytheoretic characterizations of heterotic models of computation, introduced by Stepney et al., combine computational models such as classical/quantum, digital/analog, synchronous/asynchronous, etc. to obtain increased computational power. A highly informative classical/quantum heterotic model of computation is represented by Abramsky's simple sequential imperative quantum programming language which extends the classical simple imperative programming language to encompass quantum computation. The mathematical (denotational) semantics of this classical language serves as a basic foundation upon which formal verification methods can be developed. We present a more comprehensive heterotic classical/quantum model of computation based on heterotic dynamical systems on convergence spaces. Convergence spaces subsume topological spaces but admit finer structure from which, in prior work, we obtained differential calculi in the cartesian closed category of convergence spaces allowing us to define heterotic dynamical systems, given by coupled systems of first order differential equations whose variables are functions from the reals to convergence spaces.
On the correspondence between quantum and classical variational principles
Ruiz, D. E.; Dodin, I. Y.
20150610
Here, classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical pointparticle and coldfluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and KleinGordon particles.
On the correspondence between quantum and classical variational principles
Ruiz, D. E.; Dodin, I. Y.
20151001
Classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical pointparticle and coldfluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and KleinGordon particles. (C) 2015 Elsevier B.V. All rights reserved.
On the correspondence between quantum and classical variational principles
NASA Astrophysics Data System (ADS)
Ruiz, D. E.; Dodin, I. Y.
20151001
Classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical pointparticle and coldfluid motion are derived from their quantum counterparts for Schrödinger, Pauli, and KleinGordon particles.
Quantumclassical lifetimes of Rydberg molecules
NASA Astrophysics Data System (ADS)
Junginger, Andrej; Main, Jörg; Wunner, Günter
20130401
A remarkable property of Rydberg atoms is the possibility of creating molecules formed by one highly excited atom and another atom in the ground state. The first realization of such a Rydberg molecule has opened an active field of physical investigations, and showed that its basic properties can be described within a simple model regarding the ground state atom as a small perturber that is bound by a lowenergy scattering process with the Rydberg electron (Greene et al 2000 Phys. Rev. Lett. 85 2458). Besides the good agreement between theory and the experiment concerning the vibrational states of the molecule, the experimental observations yield the astonishing feature that the lifetime of the molecule is clearly reduced as compared to the bare Rydberg atom (Butscher et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 184004). With focus on this yet unexplained observation, we investigate in this paper the vibrational ground state of the molecule in a quantumclassical framework. We show that the Rydberg wavefunction is continuously detuned by the presence of the moving ground state atom and that the timescale on which the detuning significantly exceeds the natural linewidth is in good agreement with the observed reduced lifetimes of the Rydberg molecule.
Classical and quantum superintegrability with applications
NASA Astrophysics Data System (ADS)
Miller, Willard, Jr.; Post, Sarah; Winternitz, Pavel
20131001
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and integrals of motion that are polynomials in the momenta. We present a classification of secondorder superintegrable systems in twodimensional Riemannian and pseudoRiemannian spaces. It is based on the study of the quadratic algebras of the integrals of motion and on the equivalence of different systems under coupling constant metamorphosis. The determining equations for the existence of integrals of motion of arbitrary order in real Euclidean space E2 are presented and partially solved for the case of thirdorder integrals. A systematic exposition is given of systems in two and higher dimensional space that allow integrals of arbitrary order. The algebras of integrals of motions are not necessarily quadratic but close polynomially or rationally. The relation between superintegrability and the classification of orthogonal polynomials is analyzed.
Embedding quantum into classical: contextualization vs conditionalization.
Dzhafarov, Ehtibar N; Kujala, Janne V
20140101
We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is "automatically" labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Belltype inequalities or quantummechanical constraints). In the conditionalization approach one considers the conditions under which the random variables are recorded as if they were values of another random variable, so that the observed distributions are interpreted as conditional ones. This approach is uninformative with respect to relations between the distributions observed under different conditions because any set of such distributions is compatible with any distribution assigned to the conditions. PMID:24681665
Embedding Quantum into Classical: Contextualization vs Conditionalization
Dzhafarov, Ehtibar N.; Kujala, Janne V.
20140101
We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is “automatically” labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Belltype inequalities or quantummechanical constraints). In the conditionalization approach one considers the conditions under which the random variables are recorded as if they were values of another random variable, so that the observed distributions are interpreted as conditional ones. This approach is uninformative with respect to relations between the distributions observed under different conditions because any set of such distributions is compatible with any distribution assigned to the conditions. PMID:24681665
Opening up three quantum boxes causes classically undetectable wavefunction collapse
George, Richard E.; Robledo, Lucio M.; Maroney, Owen J. E.; Blok, Machiel S.; Bernien, Hannes; Markham, Matthew L.; Twitchen, Daniel J.; Morton, John J. L.; Briggs, G. Andrew D.; Hanson, Ronald
20130101
One of the most striking features of quantum mechanics is the profound effect exerted by measurements alone. Sophisticated quantum control is now available in several experimental systems, exposing discrepancies between quantum and classical mechanics whenever measurement induces disturbance of the interrogated system. In practice, such discrepancies may frequently be explained as the backaction required by quantum mechanics adding quantum noise to a classical signal. Here, we implement the “threebox” quantum game [Aharonov Y, et al. (1991) J Phys A Math Gen 24(10):2315–2328] by using stateoftheart control and measurement of the nitrogen vacancy center in diamond. In this protocol, the backaction of quantum measurements adds no detectable disturbance to the classical description of the game. Quantum and classical mechanics then make contradictory predictions for the same experimental procedure; however, classical observers are unable to invoke measurementinduced disturbance to explain the discrepancy. We quantify the residual disturbance of our measurements and obtain data that rule out any classical model by ≳7.8 standard deviations, allowing us to exclude the property of macroscopic state definiteness from our system. Our experiment is then equivalent to the test of quantum noncontextuality [Kochen S, Specker E (1967) J Math Mech 17(1):59–87] that successfully addresses the measurement detectability loophole. PMID:23412336
Quasisuperactivation for the classical capacity of quantum channels
Gyongyosi, Laszlo; Imre, Sandor
20141204
The superactivation effect has its roots in the extreme violation of additivity of the channel capacity and enables to reliably transmit quantum information over zerocapacity quantum channels. In this work we demonstrate a similar effect for the classical capacity of a quantum channel which previously was thought to be impossible.
Macroscopicity and classicality of quantum fluctuations in de Sitter space
Wada, S.
19880801
On the basis of the nonprobabilistic interpretation of quantum mechanics, the authors define ''macroscopicity'' and ''classicality'' of quantum fluctuations as closely related but separate concepts. Then these properties are examined in quantum states (wave functions) of matter fields in de Sitter spacetime.
Arbitrated quantum signature of classical messages without using authenticated classical channels
NASA Astrophysics Data System (ADS)
Luo, YiPing; Hwang, Tzonelih
20140101
This paper points out design confusion existing in all the arbitrated quantum signatures (AQS) that require public discussions over authenticated classical channels. Instead, an AQS scheme of classical messages without using authenticated classical channels is proposed here. A cryptographic hash function is used in combine with quantum mechanics to check the existence of an eavesdropping or to verify a signature. In addition, by using only single photons, this scheme provides higher efficiency both in quantum transmissions and generations. The proposed AQS scheme is shown to be immune to several wellknown attacks, i.e., the Trojanhorse attacks and the existential forgery attack.
Interpretation neutrality in the classical domain of quantum theory
NASA Astrophysics Data System (ADS)
Rosaler, Joshua
20160201
I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de BroglieBohm and GRW interpretations. I further show that this interpretationneutral, decoherencebased account conforms to a general view of intertheoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretationneutral account rests on a general threepronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherencecompatible mechanism for collapse. It also incorporates a novel argument as to why branchrelative trajectories should be approximately Newtonian, which is based on a littlediscussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closedsystems version. In the Conclusion, I briefly suggest how the strategy for quantumclassical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity.
Models on the boundary between classical and quantum mechanics.
Hooft, Gerard 't
20150801
Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened. PMID:26124246
Twoslit experiment: quantum and classical probabilities
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
20150601
Interrelation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantumclassical interrelation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the twoslit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the twoslit experiment have the nonKolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the nonclassicality of quantum probability. We compare this embedding of nonKolmogorovian quantum probabilities into the Kolmogorov model with wellknown embeddings of nonEuclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane).
Classical and quantum distinctions between weak and strong coupling
NASA Astrophysics Data System (ADS)
RahimzadehKalaleh Rodriguez, Said
20160301
Coupled systems subject to dissipation exhibit two different regimes known as weak coupling and strong coupling. Two damped coupled harmonic oscillators (CHOs) constitute a model system where the key features of weak and strong coupling can be identified. Several of these features are common to classical and quantum systems, as a number of quantumclassical correspondences have shown. However, the condition defining the boundary between weak and strong coupling is distinct in classical and quantum formalisms. Here we describe the origin of two widely used definitions of strong coupling. Using a classical CHO model, we show that energy exchange cycles and avoided resonance crossings signal the onset of strong coupling according to one criterion. From the classical CHO model we derive a nonHermitian Hamiltonian describing open quantum systems. Based on the analytic properties of the Hamiltonian, we identify the boundary between weak and strong coupling with a different feature: a nonHermitian degeneracy known as the exceptional point. For certain parameter ranges the classical and quantum criterion for strong coupling coincide; for other ranges they do not. Examples of systems in strong coupling according to one or another criterion, but not both, are illustrated. The framework here presented is suitable for introducing graduate or advanced undegraduate students to the basic properties of strongly coupled systems, as well as to the similarities and subtle differences between classical and quantum descriptions of coupled dissipative systems.
Quantumclassical correspondence in steady states of nonadiabatic systems
Fujii, Mikiya; Yamashita, Koichi
20151231
We first present nonadiabatic path integral which is exact formulation of quantum dynamics in nonadiabatic systems. Then, by applying the stationary phase approximations to the nonadiabatic path integral, a semiclassical quantization condition, i.e., quantumclassical correspondence, for steady states of nonadiabatic systems is presented as a nonadiabatic trace formula. The present quantumclassical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow degree of freedom, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels.
Sharing of classical and quantum correlations via XY interaction
Wang, Jieci; Silva, Jaime; LancerosMendez, Senentxu
20140915
The sharing of classical and quantum correlations via XY interaction is investigated. The model includes two identical networks consisting of n nodes, the ith node of one network sharing a correlated state with the jth node of the other network, while all other nodes are initially unconnected. It is shown that classical correlation, quantum discord as well as entanglement can be shared between any two nodes of the network via XY interaction and that quantum information can be transferred effectively between them. It is found that there is no simple dominating relation between the quantum correlation and entanglement in inertial system.
Entanglement, the quantum formalism and the classical world
Matzkin, A.
20110923
75 years after the term 'entanglement' was coined to a peculiar feature inherent to quantum systems, the connection between quantum and classical mechanics remains an open problem. Drawing on recent results obtained in semiclassical systems, we discuss here the fate of entanglement in a closed system as Planck's constant becomes vanishingly small. In that case the generation of entanglement in a quantum system is perfectly reproduced by properly defined correlations of the corresponding classical system. We speculate on what these results could imply regarding the status of entanglement and of the ensuing quantum correlations.
Is classical flat Kasner spacetime flat in quantum gravity?
NASA Astrophysics Data System (ADS)
Singh, Parampreet
20160501
Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology (LQC). We find that even though the spacetime curvature vanishes at the classical level, nontrivial quantum gravitational effects can arise. For the standard loop quantization of BianchiI spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a physical solution of the effective spacetime description, except in a limit. The lack of a flat Kasner metric at the quantum level results from a novel feature of the loop quantum BianchiI spacetime: quantum geometry induces nonvanishing spacetime curvature components, making it not Ricci flat even when no matter is present. The noncurvature singularity of the classical flat Kasner spacetime is avoided, and the effective spacetime transits from a flat Kasner spacetime in asymptotic future, to a Minkowski spacetime in asymptotic past. Interestingly, for an alternate loop quantization which does not share some of the fine features of the standard quantization, flat Kasner spacetime with expected classical features exists. In this case, even with nontrivial quantum geometric effects, the spacetime curvature vanishes. These examples show that the character of even a flat classical vacuum spacetime can alter in a fundamental way in quantum gravity and is sensitive to the quantization procedure.
QuantumClassical Nonadiabatic Dynamics: Coupled vs IndependentTrajectory Methods.
Agostini, Federica; Min, Seung Kyu; Abedi, Ali; Gross, E K U
20160510
Trajectorybased mixed quantumclassical approaches to coupled electronnuclear dynamics suffer from wellstudied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfestlike dynamics. In the context of electronic nonadiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper, we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electronnuclear wave function. We present a simple quantumclassical scheme based on coupled classical trajectories and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the abovementioned traditional methods. PMID:27030209
Glover, William J; Larsen, Ross E; Schwartz, Benjamin J
20081028
The chargetransfertosolvent (CTTS) reactions of solvated atomic anions serve as ideal models for studying the dynamics of electron transfer: The fact that atomic anions have no internal degrees of freedom provides one of the most direct routes to understanding how the motions of solvent molecules influence charge transfer, and the relative simplicity of atomic electronic structure allows for direct contact between theory and experiment. To date, molecular dynamics simulations of the CTTS process have relied on a singleelectron description of the atomic aniononly the electron involved in the charge transfer has been treated quantum mechanically, and the electronic structure of the atomic solute has been treated via pseudopotentials. In this paper, we examine the severity of approximating the electronic structure of CTTS anions with a oneelectron model and address the role of electronic exchange and correlation in both CTTS electronic structure and dynamics. To do this, we perform manyelectron mixed quantum/classical molecular dynamics simulations of the ground and excitedstate properties of the aqueous sodium anion (sodide). We treat both of the sodide valence electrons quantum mechanically and solve the Schrodinger equation using configuration interaction with singles and doubles (CISD), which provides an exact solution for two electrons. We find that our multielectron simulations give excellent general agreement with experimental results on the CTTS spectroscopy and dynamics of sodide in related solvents. We also compare the results of our multielectron simulations to those from oneelectron simulations on the same system [C. J. Smallwood et al., J. Chem. Phys. 119, 11263 (2003)] and find substantial differences in the equilibrium CTTS properties and the nonadiabatic relaxation dynamics of one and twoelectron aqueous sodide. For example, the oneelectron model substantially underpredicts the size of sodide, which in turn results in a dramatically
NASA Astrophysics Data System (ADS)
Glover, William J.; Larsen, Ross E.; Schwartz, Benjamin J.
20081001
The chargetransfertosolvent (CTTS) reactions of solvated atomic anions serve as ideal models for studying the dynamics of electron transfer: The fact that atomic anions have no internal degrees of freedom provides one of the most direct routes to understanding how the motions of solvent molecules influence charge transfer, and the relative simplicity of atomic electronic structure allows for direct contact between theory and experiment. To date, molecular dynamics simulations of the CTTS process have relied on a singleelectron description of the atomic anion—only the electron involved in the charge transfer has been treated quantum mechanically, and the electronic structure of the atomic solute has been treated via pseudopotentials. In this paper, we examine the severity of approximating the electronic structure of CTTS anions with a oneelectron model and address the role of electronic exchange and correlation in both CTTS electronic structure and dynamics. To do this, we perform manyelectron mixed quantum/classical molecular dynamics simulations of the ground and excitedstate properties of the aqueous sodium anion (sodide). We treat both of the sodide valence electrons quantum mechanically and solve the Schrödinger equation using configuration interaction with singles and doubles (CISD), which provides an exact solution for two electrons. We find that our multielectron simulations give excellent general agreement with experimental results on the CTTS spectroscopy and dynamics of sodide in related solvents. We also compare the results of our multielectron simulations to those from oneelectron simulations on the same system [C. J. Smallwood et al., J. Chem. Phys. 119, 11263 (2003)] and find substantial differences in the equilibrium CTTS properties and the nonadiabatic relaxation dynamics of one and twoelectron aqueous sodide. For example, the oneelectron model substantially underpredicts the size of sodide, which in turn results in a dramatically
Entropies and correlations in classical and quantum systems
NASA Astrophysics Data System (ADS)
Man'ko, Margarita A.; Man'ko, Vladimir I.; Marmo, Giuseppe
20160901
We present a review of entropy properties for classical and quantum systems including Shannon entropy, von Neumann entropy, Rényi entropy, and Tsallis entropy. We discuss known and new entropic and information inequalities for classical and quantum systems, both composite and noncomposite. We demonstrate matrix inequalities associated with the entropic subadditivity and strong subadditivity conditions and give a new inequality for matrix elements of unitary matrices.
Geodesics in information geometry: classical and quantum phase transitions.
Kumar, Prashant; Mahapatra, Subhash; Phukon, Prabwal; Sarkar, Tapobrata
20121101
We study geodesics on the parameter manifold for systems exhibiting second order classical and quantum phase transitions. The coupled nonlinear geodesic equations are solved numerically for a variety of models which show such phase transitions in the thermodynamic limit. It is established that both in the classical as well as in the quantum cases, geodesics are confined to a single phase and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems. PMID:23214748
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T.
20140315
The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the BoseEinstein statistics with the related problem of the condensation and the FermiDirac statistics.
The structure of classical extensions of quantum probability theory
NASA Astrophysics Data System (ADS)
Stulpe, Werner; Busch, Paul
20080301
On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the socalled MisraBugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hiddenvariable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed.
PREFACE: Particles and Fields: Classical and Quantum
NASA Astrophysics Data System (ADS)
Asorey, M.; ClementeGallardo, J.; Marmo, G.
20070701
This volume contains some of the contributions to the Conference Particles and Fields: Classical and Quantum, which was held at Jaca (Spain) in September 2006 to honour George Sudarshan on his 75th birthday. Former and current students, associates and friends came to Jaca to share a few wonderful days with George and his family and to present some contributions of their present work as influenced by George's impressive achievements. This book summarizes those scientific contributions which are presented as a modest homage to the master, collaborator and friend. At the social ceremonies various speakers were able to recall instances of his lifelong activity in India, the United States and Europe, adding colourful remarks on the friendly and intense atmosphere which surrounded those collaborations, some of which continued for several decades. This meeting would not have been possible without the financial support of several institutions. We are deeply indebted to Universidad de Zaragoza, Ministerio de Educación y Ciencia de España (CICYT), Departamento de Ciencia, Tecnología y Universidad del Gobierno de Aragón, Universitá di Napoli 'Federico II' and Istituto Nazionale di Fisica Nucleare. Finally, we would like to thank the participants, and particularly George's family, for their contribution to the wonderful atmosphere achieved during the Conference. We would like also to acknowledge the authors of the papers collected in the present volume, the members of the Scientific Committee for their guidance and support and the referees for their generous work. M Asorey, J ClementeGallardo and G Marmo The Local Organizing Committee George Sudarshan
A. Ashtekhar (Pennsylvania State University, USA)  
L. J. Boya (Universidad de Zaragoza, Spain)  
I. Cirac (Max Planck Institute, Garching
Communication Tasks with Infinite QuantumClassical Separation. Perry, Christopher; Jain, Rahul; Oppenheim, Jonathan 20150717 Quantum resources can be more powerful than classical resourcesa quantum computer can solve certain problems exponentially faster than a classical computer, and computing a function of two parties' inputs can be done with exponentially less communication with quantum messages than with classical ones. Here we consider a task between two players, Alice and Bob where quantum resources are infinitely more powerful than their classical counterpart. Alice is given a string of length n, and Bob's task is to exclude certain combinations of bits that Alice might have. If Alice must send classical messages, then she must reveal nearly n bits of information to Bob, but if she is allowed to send quantum bits, the amount of information she must reveal goes to zero with increasing n. Next, we consider a version of the task where the parties may have access to entanglement. With this assistance, Alice only needs to send a constant number of bits, while without entanglement, the number of bits Alice must send grows linearly with n. The task is related to the PuseyBarrettRudolph theorem which arises in the context of the foundations of quantum theory. PMID:26230777 Maximal Parrondo's Paradox for Classical and Quantum Markov Chains NASA Astrophysics Data System (ADS) Grünbaum, F. Alberto; Pejic, Michael 20160201 Parrondo's paradox refers to the situation where two, multiround games with a fixed winning criteria, both with probability greater than onehalf for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probability greater than onehalf. In this paper, we will analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox. The game we have utilized is simpler than games for which this behavior has been previously noted in the classical and quantum cases. We will show that in certain situations the paradox can occur to a greater degree in the quantum version than is possible in the classical versions. Classical and quantum mechanical motion in magnetic fields NASA Astrophysics Data System (ADS) Franklin, J.; Cole Newton, K. 20160401 We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For fluxfree radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds depend, classically, on a gaugefixed magnetic vector potential, and we demonstrate some trajectories associated with this special type of magnetic field. Then we show that some of the geometric features of the classical trajectory (perpendicular exit from the field region, trapped and escape behavior) are reproduced quantum mechanically, using a numerical method that extends the normpreserving CrankNicolson method to problems involving magnetic fields. While there are similarities between the classical trajectory and the position expectation value of the quantummechanical solution, there are also differences, and we demonstrate some of these. Classical and Quantum Mechanical Motion in Magnetic Fields NASA Astrophysics Data System (ADS) Newton, K. Cole; Franklin, Joel 20160301 We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For fluxfree radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds depend, classically, on a gaugefixed magnetic vector potential, and demonstrate some trajectories associated with this special type of magnetic field. Then we show that some of the geometric features of the classical trajectory (perpendicular exit from the field region, trapped and escape behavior) are reproduced quantum mechanically using a numerical method that extends the normpreserving CrankNicolson method to problems involving magnetic fields. While there are similarities between the classical trajectory and the position expectation value of the quantum mechanical solution, there are also differences, and we demonstrate some of these. A wave equation interpolating between classical and quantum mechanics NASA Astrophysics Data System (ADS) Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O. 20151001 We derive a ‘master’ wave equation for a family of complexvalued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the HamiltonJacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of manybody theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in nonrelativistic and relativistic quantum field theory. Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations. Marcuzzi, Matteo; Buchhold, Michael; Diehl, Sebastian; Lesanovsky, Igor 20160617 Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states. PMID:27367395 Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations NASA Astrophysics Data System (ADS) Marcuzzi, Matteo; Buchhold, Michael; Diehl, Sebastian; Lesanovsky, Igor 20160601 Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states. Information security: from classical to quantum NASA Astrophysics Data System (ADS) Barnett, Stephen M.; Brougham, Thomas 20120901 Quantum cryptography was designed to provide a new approach to the problem of distributing keys for privatekey cryptography. The principal idea is that security can be ensured by exploiting the laws of quantum physics and, in particular, by the fact that any attempt to measure a quantum state will change it uncontrollably. This change can be detected by the legitimate users of the communication channel and so reveal to them the presence of an eavesdropper. In this paper I explain (briefly) how quantum key distribution works and some of the progress that has been made towards making this a viable technology. With the principles of quantum communication and quantum key distribution firmly established, it is perhaps time to consider how efficient it can be made. It is interesting to ask, in particular, how many bits of information might reasonably be encoded securely on each photon. The use of photons entangled in their time of arrival might make it possible to achieve data rates in excess of 10 bits per photon. Planck's radiation law: is a quantumclassical perspective possible? NASA Astrophysics Data System (ADS) Marrocco, Michele 20160501 Planck's radiation law provides the solution to the blackbody problem that marks the decline of classical physics and the rise of the quantum theory of the radiation field. Here, we venture to suggest the possibility that classical physics might be equally suitable to deal with the blackbody problem. A classical version of the Planck's radiation law seems to be achievable if we learn from the quantumclassical correspondence between classical Mie theory and quantummechanical wave scattering from spherical scatterers (partial wave analysis). This correspondence designs a procedure for countable energy levels of the radiation trapped within the blackbody treated within the multipole approach of classical electrodynamics (in place of the customary and problematic expansion in terms of plane waves that give rise to the ultraviolet catastrophe). In turn, introducing the Boltzmann discretization of energy levels, the tools of classical thermodynamics and statistical theory become available for the task. On the other hand, the final result depends on a free parameter whose physical units are those of an action. Tuning this parameter on the value given by the Planck constant makes the classical result agree with the canonical Planck's radiation law. Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates NASA Astrophysics Data System (ADS) Bravyi, Sergey; Gosset, David 20160601 We present a new algorithm for classical simulation of quantum circuits over the Clifford+T gate set. The runtime of the algorithm is polynomial in the number of qubits and the number of Clifford gates in the circuit but exponential in the number of T gates. The exponential scaling is sufficiently mild that the algorithm can be used in practice to simulate mediumsized quantum circuits dominated by Clifford gates. The first demonstrations of faulttolerant quantum circuits based on 2D topological codes are likely to be dominated by Clifford gates due to a high implementation cost associated with logical T gates. Thus our algorithm may serve as a verification tool for nearterm quantum computers which cannot in practice be simulated by other means. To demonstrate the power of the new method, we performed a classical simulation of a hidden shift quantum algorithm with 40 qubits, a few hundred Clifford gates, and nearly 50 T gates. Quantum Plasma Effects in the Classical Regime Brodin, G.; Marklund, M.; Manfredi, G. 20080502 For quantum effects to be significant in plasmas it is often assumed that the temperature over density ratio must be small. In this paper we challenge this assumption by considering the contribution to the dynamics from the electron spin properties. As a starting point we consider a multicomponent plasma model, where electrons with spinup and spindown are regarded as different fluids. By studying the propagation of Alfven wave solitons we demonstrate that quantum effects can survive in a relatively hightemperature plasma. The consequences of our results are discussed. Quantum stochastic walks: A generalization of classical random walks and quantum walks NASA Astrophysics Data System (ADS) Whitfield, James D.; RodríguezRosario, César A.; AspuruGuzik, Alán 20100201 We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantummechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantumstochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QWtoCRW transition. Relativistic classical integrable tops and quantum Rmatrices NASA Astrophysics Data System (ADS) Levin, A.; Olshanetsky, M.; Zotov, A. 20140701 We describe classical toplike integrable systems arising from the quantum exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in terms of the quantum nondynamical Rmatrix even at the classical level, where the Planck constant plays the role of the relativistic deformation parameter in the sense of Ruijsenaars and Schneider (RS). The integrable systems (relativistic tops) are described as multidimensional Euler tops, and the inertia tensors are written in terms of the quantum and classical Rmatrices. A particular case of gl N system is gauge equivalent to the Nparticle RS model while a generic top is related to the spin generalization of the RS model. The simple relation between quantum Rmatrices and classical Lax operators is exploited in two ways. In the elliptic case we use the Belavin's quantum Rmatrix to describe the relativistic classical tops. Also by the passage to the noncommutative torus we study the large N limit corresponding to the relativistic version of the nonlocal 2d elliptic hydrodynamics. Conversely, in the rational case we obtain a new gl N quantum rational nondynamical Rmatrix via the relativistic top, which we get in a different way — using the factorized form of the RS Lax operator and the classical Symplectic Hecke (gauge) transformation. In particular case of gl2 the quantum rational Rmatrix is 11vertex. It was previously found by Cherednik. At last, we describe the integrable spin chains and Gaudin models related to the obtained Rmatrix. Electromagnetically induced classical and quantum Lau effect NASA Astrophysics Data System (ADS) Qiu, Tianhui; Yang, Guojian; Xiong, Jun; Xu, Deqin 20160701 We present two schemes of Lau effect for an object, an electromagnetically induced grating generated based on the electromagnetically induced effect. The Lau interference pattern is detected either directly in the way of the traditional Lau effect measurement with a classical thermal light being the imaging light, or indirectly and nonlocally in the way of twophoton coincidence measurement with a pair of entangled photons being the imaging light. Observation of Quantum Fingerprinting Beating the Classical Limit NASA Astrophysics Data System (ADS) Guan, JianYu; Xu, Feihu; Yin, HuaLei; Li, Yuan; Zhang, WeiJun; Chen, SiJing; Yang, XiaoYan; Li, Li; You, LiXing; Chen, TengYun; Wang, Zhen; Zhang, Qiang; Pan, JianWei 20160601 Quantum communication has historically been at the forefront of advancements, from fundamental tests of quantum physics to utilizing the quantummechanical properties of physical systems for practical applications. In the field of communication complexity, quantum communication allows the advantage of an exponential reduction in the transmitted information over classical communication to accomplish distributed computational tasks. However, to date, demonstrating this advantage in a practical setting continues to be a central challenge. Here, we report a proofofprinciple experimental demonstration of a quantum fingerprinting protocol that for the first time surpasses the ultimate classical limit to transmitted information. Ultralow noise superconducting singlephoton detectors and a stable fiberbased Sagnac interferometer are used to implement a quantum fingerprinting system that is capable of transmitting less information than the classical proven lower bound over 20 km standard telecom fiber for input sizes of up to 2 Gbits. The results pave the way for experimentally exploring the advanced features of quantum communication and open a new window of opportunity for research in communication complexity and testing the foundations of physics.
