Stereodynamics of chemical reactions: quasiclassical, quantum and mixed quantumclassical theories
NASA Astrophysics Data System (ADS)
Xu, Wenwu; Zhao, Guangjiu
20120401
In this review, some benchmark works by Han and coworkers on the stereodynamics of typical chemical reactions, triatomic reactions H + D2, Cl + H2 and O + H2 and polyatomic reaction Cl+CH4/CD4, are presented by using the quasiclassical, quantum and mixed quantumclassical methods. The product alignment and orientation in these A+BC model reactions are discussed in detail. We have also compared our theoretical results with experimental measurements and demonstrated that our theoretical results are in good agreement with the experimental results. Quasiclassical trajectory (QCT) method ignores some quantum effects like the tunneling effect and zeropoint energy. The quantum method will be very timeconsuming. Moreover, the mixed quantumclassical method can take into account some quantum effects and hence is expected to be applicable to large systems and widely used in chemical stereodynamics studies.
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.
HighNOON states by mixing quantum and classical light.
Afek, Itai; Ambar, Oron; Silberberg, Yaron
20100514
Precision measurements can be brought to their ultimate limit by harnessing the principles of quantum mechanics. In optics, multiphoton entangled states, known as NOON states, can be used to obtain highprecision phase measurements, becoming more and more advantageous as the number of photons grows. We generated "highNOON" states (N = 5) by multiphoton interference of quantum downconverted light with a classical coherent state in an approach that is inherently scalable. Superresolving phase measurements with up to five entangled photons were produced with a visibility higher than that obtainable using classical light only.
Mixed quantumclassical dynamics for charge transport in organics.
Wang, Linjun; Prezhdo, Oleg V; Beljonne, David
20150521
Charge transport plays a crucial role in the working principle of most optoelectronic and energy devices. This is especially true for organic materials where the first theoretical models date back to the 1950s and have continuously evolved ever since. Most of these descriptions rely on perturbation theory to treat small interactions in the Hamiltonian. In particular, applying a perturbative treatment to the electronphonon and electronelectron coupling results in the band and hopping models, respectively, the signature of which is conveyed by a characteristic temperature dependence of mobility. This perspective describes recent progress of studying charge transport in organics using mixed quantumclassical dynamics techniques, including mean field and surface hopping theories. The studies go beyond the perturbation treatments and represent the processes explicitly in the timedomain, as they occur in real life. The challenges, advantages, and disadvantages of both approaches are systematically discussed. Special focus is dedicated to the temperature dependence of mobility, the role of local and nonlocal electronphonon couplings, as well as the interplay between electronic and electronphonon interactions.
Classicaltoquantum transition with broadband fourwave mixing.
Vered, Rafi Z; Shaked, Yaakov; BenOr, Yelena; Rosenbluh, Michael; Pe'er, Avi
20150213
A key question of quantum optics is how nonclassical biphoton correlations at low power evolve into classical coherence at high power. Direct observation of the crossover from quantum to classical behavior is desirable, but difficult due to the lack of adequate experimental techniques that cover the ultrawide dynamic range in photon flux from the single photon regime to the classical level. We investigate biphoton correlations within the spectrum of light generated by broadband fourwave mixing over a large dynamic range of ∼80 dB in photon flux across the classicaltoquantum transition using a twophoton interference effect that distinguishes between classical and quantum behavior. We explore the quantumclassical nature of the light by observing the interference contrast dependence on internal loss and demonstrate quantum collapse and revival of the interference when the fourwave mixing gain in the fiber becomes imaginary.
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.
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. PMID:25978878
Hsieh, ChangYu; Kapral, Raymond
20130401
Mixed quantumclassical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forwardbackward trajectory solution of the mixed quantumclassical Liouville equation in the mapping basis [C.Y. Hsieh and R. Kapral, J. Chem. Phys. 137, 22A507 (2012)] is one such scheme. It simulates the dynamics via the propagation of forward and backward trajectories of quantum coherent state variables, and the propagation of bath trajectories on a meanfield potential determined jointly by the forward and backward trajectories. An analysis of the properties of this solution, numerical tests of its validity and an investigation of its utility for the study of nonadiabtic quantum processes are given. In addition, we present an extension of this approximate solution that allows one to systematically improve the results. This extension, termed the jump forwardbackward trajectory solution, is analyzed and tested in detail and its various implementations are discussed. PMID:23574211
Semenov, Alexander; Babikov, Dmitri
20140116
For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with fullquantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the fullquantum framework.
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.
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.
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
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.
Multipartite quantum and classical correlations in symmetric nqubit mixed states
NASA Astrophysics Data System (ADS)
Giorgi, Gian Luca; Campbell, Steve
20160801
We discuss how to calculate genuine multipartite quantum and classical correlations in symmetric, spatially invariant, mixed nqubit density matrices. We show that the existence of symmetries greatly reduces the amount of free parameters to be optimized in order to find the optimal measurement that minimizes the conditional entropy in the discord calculation. We apply this approach to the states exhibited dynamically during a thermodynamic protocol to extract maximum work. We also apply the symmetry criterion to a wide class of physically relevant cases of spatially homogeneous noise over multipartite entangled states. Exploiting symmetries we are able to calculate the nonlocal and genuine quantum features of these states and note some interesting properties.
Megow, Jörg; Röder, Beate; Kulesza, Alexander; BonačićKoutecký, Vlasta; May, Volkhard
20110225
Electronic excitation energy transfer (EET) is described theoretically for the chromophore complex P(4) formed by a butanediamine dendrimer to which four pheophorbidea molecules are covalently linked. To achieve a description with atomic resolution, and to account for the effect of an ethanol solvent, a mixed quantumclassical methodology is utilized. Roomtemperature molecular dynamics simulations are used to describe the nuclear dynamics, and EET is accounted for in utilizing a mixed quantumclassical formulation of the transition rates. Therefore, the full quantum expression of the EET rates is given and the change to a mixed quantumclassical version is briefly explained. The description results in the calculation of transition rates which coincide rather satisfactory with available experimental data on P(4). It is also shown that different assumptions of classical Förster theory are not valid for P(4). The temporal behavior of EET deduced from the rate equations is confronted with that following from the solution of the timedependent Schrödinger equation entering the mixed quantumclassical description of EET. From this we can conclude that EET in flexible chromophore complexes such as P(4) can be rather satisfactory estimated by single transition rates. A correct description, however, is only achievable by using a sufficiently large set of rates that correspond to the various possible equilibrium configurations of the complex.
Quantum computing classical physics.
Meyer, David A
20020315
In the past decade, quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do soquantum latticegas automataand show how to implement them efficiently on standard quantum computers.
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.
A test of the possibility of calculating absorption spectra by mixed quantumclassical methods
NASA Astrophysics Data System (ADS)
Haug, Kenneth; Metiu, Horia
19921001
Some of the most efficient methods for studying systems having a large number of degrees of freedom treat a few degrees of freedom quantum mechanically and the remainder classically. Here we examine how these methods fare when used to calculate the cross section for photon absorption by a quantum system imbedded in a medium. To test the method, we study a model which has two degrees of freedom and mimicks the properties of a onedimensional alkali atomHe dimer. We treat the electron motion quantum mechanically and the distance between the He atom and the alkali ion classically. Light absorption occurs because the electron is coupled to radiation. The calculation of the absorption cross section by quantumclassical methods fails rather dramaticallyat certain frequencies, the absorption coefficient is negative. By comparing with exact quantum calculations, we show that this failure takes place because the time evolution of the classical variables influences the dynamics of the quantum degree of freedom through the Hamiltonian only; important information, which a fully quantum treatment would put in the wave function, is missing. To repair this flaw, we experiment with a method which uses a swarm of classical trajectories to generate a ``classical wave function.'' The results are encouraging, but require substantial computer time when the number of classical variables is large. We argue that in the limit of many classical degrees of freedom, accurate calculations can be performed by using the timedependent Hartree method and treating some degrees of freedom by exact numerical methods (e.g., a fast Fourier transform procedure) and the others by Gaussian wave packets or any other propagation method that is accurate for a very short time. This procedure leads to a simple time domain picture of dephasing and line broadening in the case of a localized quantum system imbedded in a medium with heavy atoms.
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
Randomness: Quantum versus classical
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
20160501
Recent tremendous development of quantum information theory has led to a number of quantum technological projects, e.g. quantum random generators. This development had stimulated a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is the elaboration of a consistent and commonly accepted interpretation of a quantum state. Closely related problem is the clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review, we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. We also discuss briefly “digital philosophy”, its role in physics (classical and quantum) and its coupling to the information interpretation of quantum mechanics (QM).
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.
Tavernelli, Ivano; Curchod, Basile F. E.; Rothlisberger, Ursula
20100515
A mixed quantumclassical method aimed at the study of nonadiabatic dynamics in the presence of external electromagnetic fields is developed within the framework of timedependent density functional theory. To this end, we use a trajectorybased description of the quantum nature of the nuclear degrees of freedom according to Tully's fewest switches trajectories surface hopping, where both the nonadiabatic coupling elements between the different potential energy surfaces, and the coupling with the external field are given as functionals of the groundstate electron density or, equivalently, of the corresponding KohnSham orbitals. The method is applied to the study of the photodissociation dynamics of some simple molecules in gas phase.
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.
NASA Astrophysics Data System (ADS)
BedardHearn, Michael J.; Larsen, Ross E.; Schwartz, Benjamin J.
20050401
In polar fluids such as water and methanol, the peak of the solvated electron's absorption spectrum in the red has been assigned as a sum of transitions between an slike ground state and three nearly degenerate plike excited states bound in a quasispherical cavity. In contrast, in weakly polar solvents such as tetrahydrofuran (THF), the solvated electron has an absorption spectrum that peaks in the midinfrared, but no definitive assignment has been offered about the origins of the spectrum or the underlying structure. In this paper, we present the results of adiabatic mixed quantum/classical molecular dynamic simulations of the solvated electron in THF, and provide a detailed explanation of the THFsolvated electron's absorption spectrum and electronic structure. Using a classical solvent model and a fully quantum mechanical excess electron, our simulations show that although the ground and first excited states are bound in a quasispherical cavity, a multitude of other, nearby solvent cavities support numerous, nearly degenerate, bound excited states that have little FranckCondon overlap with the ground state. We show that these solvent cavities, which are partially polarized so that they act as electron trapping sites, are an inherent property of the way THF molecules pack in the liquid. The absorption spectrum is thus assigned to a sum of boundtobound transitions between a localized ground state and multiple disjoint excited states scattered throughout the fluid. Furthermore, we find that the usual spherical harmonic labels (e.g., slike, plike) are not good descriptors of the excitedstate wave functions of the solvated electron in THF. Our observation of multiple disjoint excited states is consistent with femtosecond pumpprobe experiments in the literature that suggest that photoexcitation of solvated electrons in THF causes them to relocalize into solvent cavities far from where they originated.
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.
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
NASA Astrophysics Data System (ADS)
Aniello, P.; Ciaglia, F. M.; Di Cosmo, F.; Marmo, G.; PérezPardo, J. M.
20161001
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator T with a suitable realvalued function T on the space of physical states. The proper characterization of the function T relies on a particular relation with the dynamical evolution of the system rather than with the infinitesimal generator of the dynamics (Hamiltonian). We first consider the case of classical hamiltonian mechanics, where observables are functions on phase space and the tools of differential geometry can be applied. The idea is then extended to the case of the unitary evolution of pure states of finitelevel quantum systems by means of the geometric formulation of quantum mechanics. It is found that T is a function on the space of pure states which is not associated with any selfadjoint operator. The link between T and the dynamical evolution is interpreted as defining a simultaneity relation for the states of the system with respect to the dynamical evolution itself. It turns out that different dynamical evolutions lead to different notions of simultaneity, i.e., the notion of simultaneity is a dynamical notion.
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 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.
Semenov, Alexander; Ivanov, Mikhail; Babikov, Dmitri
20130821
The mixed quantum/classical approach is applied to the problem of rovibrational energy transfer in the inelastic collisions of CO(v = 1) with He atom, in order to predict the quenching rate coefficient in a broad range of temperatures 5 < T < 2500 K. Scattering calculations are done in two different ways: direct calculations of quenching cross sections and, alternatively, calculations of the excitation cross sections plus microscopic reversibility. In addition, a symmetrized averagevelocity method of Billing is tried. Combination of these methods allows reproducing experiment in a broad range of temperatures. Excellent agreement with experiment is obtained at 400 < T < 2500 K (within 10%), good agreement in the range 100 < T < 400 K (within 25%), and semiquantitative agreement at 40 < T < 100 K(within a factor of 2). This study provides a stringent test of the mixed quantum/classical theory, because the vibrational quantum in CO molecule is rather large and the quencher is very light (He atom). For heavier quenchers and closer to dissociation limit of the molecule, the mixed quantum/classical theory is expected to work even better.
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.
Classical randomness in quantum measurements
NASA Astrophysics Data System (ADS)
Mauro D'Ariano, Giacomo; Lo Presti, Paoloplacido; Perinotti, Paolo
20050701
Similarly to quantum states, also quantum measurements can be 'mixed', corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely classical nature. It is then natural to ask which apparatuses are indecomposable, i.e. do not correspond to any random choice of apparatuses. This problem is interesting not only for foundations, but also for applications, since most optimization strategies give optimal apparatuses that are indecomposable. Mathematically the problem is posed describing each measuring apparatus by a positive operatorvalued measure (POVM), which gives the statistics of the outcomes for any input state. The POVMs form a convex set, and in this language the indecomposable apparatuses are represented by extremal points—the analogous of 'pure states' in the convex set of states. Differently from the case of states, however, indecomposable POVMs are not necessarily rankone, e.g. von Neumann measurements. In this paper we give a complete classification of indecomposable apparatuses (for discrete spectrum), by providing different necessary and sufficient conditions for extremality of POVMs, along with a simple general algorithm for the decomposition of a POVM into extremals. As an interesting application, 'informationally complete' measurements are analysed in this respect. The convex set of POVMs is fully characterized by determining its border in terms of simple algebraic properties of the corresponding POVMs.
NASA Astrophysics Data System (ADS)
Kahros, Argyris
Incorporating quantum mechanics into an atomistic simulation necessarily involves solving the Schrodinger equation. Unfortunately, the computational expense associated with solving this equation scales miserably with the number of included quantum degrees of freedom (DOF). The situation is so dire, in fact, that a molecular dynamics (MD) simulation cannot include more than a small number of quantum DOFs before it becomes computationally intractable. Thus, if one were to simulate a relatively large system, such as one containing several hundred atoms or molecules, it would be unreasonable to attempt to include the effects of all of the electrons associated with all of the components of the system. The mixed quantum/classical (MQC) approach provides a way to circumvent this issue. It involves treating the vast majority of the system classically, which incurs minimal computational expense, and reserves the consideration of quantum mechanical effects for only the few degrees of freedom more directly involved in the chemical phenomenon being studied. For example, if one were to study the bonding of a single diatomic molecule in the gas phase, one could employ a MQC approach by treating the nuclei of the molecule's two atoms classicallyincluding the deeply bound, lowenergy electrons that change relatively littleand solving the Schrodinger equation only for the high energy electron(s) directly involved in the bonding of the classical cores. In such a way, one could study the bonding of this molecule in a rigorous fashion while treating only the directly related degrees of freedom quantum mechanically. Pseudopotentials are then responsible for dictating the interactions between the quantum and classical degrees of freedom. As these potentials are the sole link between the quantum and classical DOFs, their proper development is of the utmost importance. This Thesis is concerned primarily with my work on the development of novel, rigorous and dynamical
Nonclassical light for quantum information
NASA Astrophysics Data System (ADS)
Goldschmidt, Elizabeth Anne
Nonclassical light is both easily encoded with quantum information and robust against decoherence, making it a key resource that enables many quantum information applications including quantum computing, quantum communication, and quantum metrology. We present a wide range of experimental and theoretical research toward the generation, detection, characterization, and storage of nonclassical states of light with an eye toward quantum information applications. To provide a basis for the rest of the work, we begin by discussing theoretically the role of photon number statistics in optical quantum information and the use of secondorder optical coherence to characterize nonclassical light. Building on that, we present an original tool for the difficult problem of reconstructing the underlying mode distribution of multimode optical fields using simple measurements of higherorder optical coherence. We then move on to the problem of generating and storing single photons. We do this in a solidstate medium, a rareearth iondoped crystal, with a longlived spin transition ideal for storing quantum information. We experimentally demonstrate the feasibility of this concept by showing correlations between the optical fields that herald storage and retrieval of collective excitations. This scheme can be used for the two important and distinct applications of generating single photons ondemand and storing quantum information and entanglement. The detection of nonclassical light is a task as important as its generation. To this end, we study detectors with near unity detection efficiency and photon number resolution for use in quantumenabled metrology. We use such a detector to experimentally demonstrate compression of spatial fringes and investigate the possibility of improving measurement resolution with classical and nonclassical light. Finally, we report a set of experiments using photon number statistics to characterize classical and nonclassical light. We
Classical command of quantum systems.
Reichardt, Ben W; Unger, Falk; Vazirani, Umesh
20130425
Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or 'untrusted' system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantummechanical system but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantum system. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of 'untrusted' devices to establish a shared random key, with security based on the validity of quantum physics.
Classical command of quantum systems.
Reichardt, Ben W; Unger, Falk; Vazirani, Umesh
20130425
Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or 'untrusted' system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantummechanical system but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantum system. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of 'untrusted' devices to establish a shared random key, with security based on the validity of quantum physics. PMID:23619692
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 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 fields with classical perturbations
Dereziński, Jan
20140715
The main purpose of these notes is a review of various models of Quantum Field Theory (QFT) involving quadratic Lagrangians. We discuss scalar and vector bosons, spin 1/2 fermions, both neutral and charged. Beside free theories, we study their interactions with classical perturbations, called, depending on the context, an external linear source, masslike term, current or electromagnetic potential. The notes may serve as a first introduction to QFT.
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.
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.
Classical Mechanics as Nonlinear Quantum Mechanics
Nikolic, Hrvoje
20071203
All measurable predictions of classical mechanics can be reproduced from a quantumlike interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classicallike interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.
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.
Secure quantum communication using classical correlated channel
NASA Astrophysics Data System (ADS)
Costa, D.; de Almeida, N. G.; VillasBoas, C. J.
20161001
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.
Open quantum dots—probing the quantum to classical transition
NASA Astrophysics Data System (ADS)
Ferry, D. K.; Burke, A. M.; Akis, R.; Brunner, R.; Day, T. E.; Meisels, R.; Kuchar, F.; Bird, J. P.; Bennett, B. R.
20110401
Quantum dots provide a natural system in which to study both quantum and classical features of transport. As a closed testbed, they provide a natural system with a very rich set of eigenstates. When coupled to the environment through a pair of quantum point contacts, each of which passes several modes, the original quantum environment evolves into a set of decoherent and coherent states, which classically would compose a mixed phase space. The manner of this breakup is governed strongly by Zurek's decoherence theory, and the remaining coherent states possess all the properties of his pointer states. These states are naturally studied via traditional magnetotransport at low temperatures. More recently, we have used scanning gate (conductance) microscopy to probe the nature of the coherent states, and have shown that families of states exist through the spectrum in a manner consistent with quantum Darwinism. In this review, we discuss the nature of the various states, how they are formed, and the signatures that appear in magnetotransport and general conductance studies.
Yamada, Atsushi; Okazaki, Susumu
20080128
We present a quantum equation of motion for chemical reaction systems on an adiabatic doublewell potential surface in solution in the framework of mixed quantumclassical molecular dynamics, where the reactant and product states are explicitly defined by dividing the doublewell potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zeropoint energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the highenergy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.
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.
Semenov, Alexander; Babikov, Dmitri
20131107
We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the spacefixed and second in the bodyfixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the statetostate transition matrix is complexvalued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the statetostate transitions are driven by realvalued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the spacefixed formulation can serve as a test of the bodyfixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.
Hanna, Gabriel; Geva, Eitan
20080401
The vibrational energy relaxation (VER) of the hydrogen stretch in a linear hydrogenbonded complex dissolved in a polar solvent is studied. The study is based on the AzzouzBorgis model [Azzouz, H.; Borgis, D. J. Chem. Phys. 1993, 98, 7361], which is known to account for many important features of real hydrogenbonded systems, including ionictocovalent tautomerism and a broad distribution of hydrogen stretch frequencies. A description of VER in this strongly coupled system is considered, which consists of the following three consecutive steps: (1) solvation on the adiabatic excited vibrational surface; (2) nonadiabatic transition from the excited to the ground adiabatic vibrational surface; and (3) solvation on the adiabatic ground vibrational surface. The relaxation dynamics during those three steps were simulated via the mixed quantumclassical Liouville method, where the hydrogen is treated quantummechanically, while the other particles are treated in a classicallike manner. The solvation on the excitedstate surface was found to occur rapidly ( approximately 0.5 ps) and to involve energy exchange with both the intramolecular and intermolecular degrees of freedom. It was also found that, while energy is released to the solvent during the solvation of the covalent tautomer, the solvation of the ionic tautomer involves absorption of energy from the solvent. The decrease in the transition frequency during the solvation process also facilitates the nonadiabatic transitions, which occur rapidly ( approximately 0.8 ps) thereafter. The nonadiabatic transitions were shown to be induced by interactions with a large number of solvent molecules and to be relatively insensitive to their location relative to the complex. Finally, solvation on the groundstate surface was seen to occur on a time scale of approximately 1.0 ps and leads to nonequilibrium ionic and covalent subpopulations. Equilibration on the groundstate surface occurs on a significantly slower time scale
From quantum ladder climbing to classical autoresonance
Marcus, G.; Friedland, L.; Zigler, A.
20040101
The autoresonance phenomenon allows excitation of a classical, oscillatory nonlinear system to high energies by using a weak, chirped frequency forcing. Ladder climbing is its counterpart in quantum mechanics. Here, for the first time to our knowledge, conditions for the transition from the quantum to the classical regimes are outlined. The similarities and differences between the two approaches are presented.
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.
Quantum entanglement capacity with classical feedback
NASA Astrophysics Data System (ADS)
Leung, Alan W.
20080101
For any quantum discrete memoryless channel, we define a quantity called quantum entanglement capacity with classical feedback (EB) , and we show that this quantity lies between two other wellstudied quantities. These two quantities—namely the quantum capacity assisted by twoway classical communication (Q2) and the quantum capacity with classical feedback (QB) —are widely conjectured to be different: There exists a quantum discrete memoryless channel for which Q2>QB . We then present a general scheme to convert any quantum errorcorrecting codes into adaptive protocols for this newly defined quantity of the quantum depolarizing channel, and illustrate with the repetition code and Shor code. We contrast the present notion with entanglement purification protocols by showing that, whilst the LeungShor protocol can be applied directly, recurrence methods need to be supplemented with other techniques but at the same time offer a way to improve the aforementioned repetition code. For the quantum depolarizing channel, we prove a formula that gives lower bounds on the quantum capacity with classical feedback from any EB protocols. We then apply this formula to the EB protocols that we discuss to obtain lower bounds on the quantum capacity with classical feedback of the quantum depolarizing channel.
Rekik, Najeh; Freedman, Holly; Hanna, Gabriel; Hsieh, ChangYu
20130414
We apply two approximate solutions of the quantumclassical Liouville equation (QCLE) in the mapping representation to the simulation of the laserinduced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the ForwardBackward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surfacehopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLEbased solutions is tested on a nontrivial electron transfer model involving more than two quantum states, a timedependent Hamiltonian, strong subsystembath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystembath coupling. In particular, we calculate the timedependent population of the photoexcited donor state in response to an ultrafast, onresonance pump pulse in a threestate model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the threestate electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLEbased surfacehopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystembath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLEbased surfacehopping results. These findings
Kwac, Kijeong; Geva, Eitan
20130627
We present a mixed quantumclassical molecular dynamics study of the nonequilibrium hydrogenbond dynamics following vibrational energy relaxation of the hydroxyl stretch in a 10 mol % methanol/carbon tetrachloride mixture and pure methanol. The ground and firstexcited energy levels and wave functions are identified with the eigenvalues and eigenfunctions of the hydroxyl's adiabatic Hamiltonian and as such depend parametrically on the configuration of the remaining, classically treated, degrees of freedom. The dynamics of the classical degrees of freedom are in turn governed by forces obtained by taking the expectation value of the force with respect to the ground or excited vibrational wave functions. Polarizable force fields and nonlinear mapping relations between the hydroxyl transition frequencies and dipole moments and the electric field along the hydroxyl bond are used, which were previously shown to quantitatively reproduce the experimental infrared steadystate absorption spectra and excited state lifetime [Kwac, K.; Geva, E. J. Phys. Chem. B 2011, 115, 9184; 2012, 116, 2856]. The relaxation from the firstexcited state to the ground state is treated as a nonadiabatic transition. Within the mixed quantumclassical treatment, relaxation from the excited state to the ground state is accompanied by a momentumjump in the classical degrees of freedom, which is in turn dictated by the nonadiabatic coupling vector. We find that the momentum jump leads to breaking of hydrogen bonds involving the relaxing hydroxyl, thereby blueshifting the transition frequency by more than the Stokes shift between the steadystate emission and absorption spectra. The subsequent nonequilibrium relaxation toward equilibrium on the ground state potential energy surface is thereby accompanied by red shifting of the transition frequency. The signature of this nonequilibrium relaxation process on the pumpprobe spectrum is analyzed in detail. The calculated pumpprobe spectrum is found
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
Unraveling Quantum Annealers using Classical Hardness.
MartinMayor, Victor; Hen, Itay
20151020
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.
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.
Shkrob, Ilya A; Glover, William J; Larsen, Ross E; Schwartz, Benjamin J
20070621
Adiabatic mixed quantum/classical (MQC) molecular dynamics (MD) simulations were used to generate snapshots of the hydrated electron in liquid water at 300 K. Water cluster anions that include two complete solvation shells centered on the hydrated electron were extracted from the MQC MD simulations and embedded in a roughly 18 Ax18 Ax18 A matrix of fractional point charges designed to represent the rest of the solvent. Density functional theory (DFT) with the BeckeLeeYangParr functional and singleexcitation configuration interaction (CIS) methods were then applied to these embedded clusters. The salient feature of these hybrid DFT(CIS)/MQC MD calculations is significant transfer (approximately 18%) of the excess electron's charge density into the 2p orbitals of oxygen atoms in OH groups forming the solvation cavity. We used the results of these calculations to examine the structure of the singly occupied and the lower unoccupied molecular orbitals, the density of states, the absorption spectra in the visible and ultraviolet, the hyperfine coupling (hfcc) tensors, and the infrared (IR) and Raman spectra of these embedded water cluster anions. The calculated hfcc tensors were used to compute electron paramagnetic resonance (EPR) and electron spin echo envelope modulation (ESEEM) spectra for the hydrated electron that compared favorably to the experimental spectra of trapped electrons in alkaline ice. The calculated vibrational spectra of the hydrated electron are consistent with the redshifted bending and stretching frequencies observed in resonance Raman experiments. In addition to reproducing the visible/near IR absorption spectrum, the hybrid DFT model also accounts for the hydrated electron's 190nm absorption band in the ultraviolet. Thus, our study suggests that to explain several important experimentally observed properties of the hydrated electron, manyelectron effects must be accounted for: oneelectron models that do not allow for mixing of the excess
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
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.``
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.
Classical and Quantum Spreading of Position Probability
ERIC Educational Resources Information Center
Farina, J. E. G.
19770101
Demonstrates that the standard deviation of the position probability of a particle moving freely in one dimension is a function of the standard deviation of its velocity distribution and time in classical or quantum mechanics. (SL)
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.
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 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.
Synchronizing quantum and classical clocks made of quantum particles
NASA Astrophysics Data System (ADS)
Flores, Philip Caesar M.; Caballar, Roland Cristopher F.; Galapon, Eric A.
20160901
We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed in Phys. Rev. A 80, 030102(R) (2009), 10.1103/PhysRevA.80.030102, can be eliminated up to a given order of ℏ by choosing an appropriate positiondependent phase for the object's wave function. This then implies that we can make the quantum arrival time of the object as close as possible to its corresponding classical arrival time, allowing us to synchronize a classical and quantum clock, which tells time using the classical and quantum arrival time of the object, respectively. We provide an example for synchronizing such a clock by making use of a quantum object with a positiondependent phase imprinted on the object's initial wave function with the use of an impulsive potential.
Unification of quantum theory and classical physics
Stapp, H.P.
19850701
A program is described for unifying quantum theory and classical physics on the basis of the Copenhageninterpretation idea of external reality and a recently discovered classical part of the electromagnetic field. The program effects an integration of the intuitions of Heisenberg, Bohr, and Einstein.
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…
Quantum Adder of Classical Numbers
NASA Astrophysics Data System (ADS)
Cherkas, A. V.; Chivilikhin, S. A.
20160801
In this article we show the precise algorithm of functioning of quantum adder on the example of addition of two 2bit numbers. It consists of the quantum Fourier transformer and conditional rotation gates that let us use the minimum number of qubits to get the addition realization of the sum. Despite the fact that the algorithm uses the minimum amount of operations this accelerates the process of the adder.
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 dynamics in adiabatic computation
NASA Astrophysics Data System (ADS)
Crowley, P. J. D.; Äńurić, T.; Vinci, W.; Warburton, P. A.; Green, A. G.
20141001
Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimization algorithms and quantum adiabatic optimization. This perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the DWave Vesuvius machine with revealing—though inconclusive—results.
Classical teleportation of a quantum Bit
Cerf; Gisin; Massar
20000313
Classical teleportation is defined as a scenario where the sender is given the classical description of an arbitrary quantum state while the receiver simulates any measurement on it. This scenario is shown to be achievable by transmitting only a few classical bits if the sender and receiver initially share local hidden variables. Specifically, a communication of 2.19 bits is sufficient on average for the classical teleportation of a qubit, when restricted to von Neumann measurements. The generalization to positiveoperatorvalued measurements is also discussed.
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.
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.
Quantum and classical opticsemerging 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 quantumclassical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.
Communication capacity of mixed quantum t designs
NASA Astrophysics Data System (ADS)
Brandsen, Sarah; Dall'Arno, Michele; Szymusiak, Anna
20160801
We operationally introduce mixed quantum t designs as the most general arbitraryrank extension of projective quantum t designs which preserves indistinguishability from the uniform distribution for t copies. First, we derive upper bounds on the classical communication capacity of any mixed t design measurement for t ∈[1 ,5 ] . Second, we explicitly compute the classical communication capacity of several mixed t design measurements, including the depolarized version of any qubit and qutrit symmetric, informationally complete (SIC) measurement and complete mutually unbiased bases, the qubit icosahedral measurement, the Hoggar SIC measurement, any antiSIC (where each element is proportional to the projector on the subspace orthogonal to one of the elements of the original SIC), and the uniform distribution over pure effects.
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.
Gaugefields and integrated quantumclassical theory
Stapp, H.P.
19860101
Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantumclassical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantumclassical connection. 17 refs.
Quantumtoclassical transition in cavity quantum electrodynamics.
Fink, J M; Steffen, L; Studer, P; Bishop, Lev S; Baur, M; Bianchetti, R; Bozyigit, D; Lang, C; Filipp, S; Leek, P J; Wallraff, A
20101015
The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the oscillator. Here, we study how the classical response of a cavity QED system emerges from the quantum one when its thermal occupationor effective temperatureis raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantumtoclassical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and timeresolved vacuum Rabi measurements.
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.
Born rule in quantum and classical mechanics
Brumer, Paul; Gong Jiangbin
20060515
Considerable effort has been devoted to deriving the Born rule [i.e., that {psi}(x){sup 2}dx is the probability of finding a system, described by {psi}, between x and x+dx] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbertspace formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.
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.
Bridging classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Haddad, D.; Seifert, F.; Chao, L. S.; Li, S.; Newell, D. B.; Pratt, J. R.; Williams, C.; Schlamminger, S.
20161001
Using a watt balance and a frequency comb, a massenergy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.
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.
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
Multitime equations, classical and quantum
Petrat, Sören; Tumulka, Roderich
20140101
Multitime equations are evolution equations involving several time variables, one for each particle. Such equations have been considered for the purpose of making theories manifestly Lorentz invariant. We compare their status and significance in classical and quantum physics. PMID:24711721
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.
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)
Quantumclassical transitions in complex networks
NASA Astrophysics Data System (ADS)
Javarone, Marco Alberto; Armano, Giuliano
20130401
The inherent properties of specific physical systems can be used as metaphors for investigation of the behavior of complex networks. This insight has already been put into practice in previous work, e.g., studying the network evolution in terms of phase transitions of quantum gases or representing distances among nodes as if they were particle energies. This paper shows that the emergence of different structures in complex networks, such as the scalefree and the winnertakesall networks, can be represented in terms of a quantumclassical transition for quantum gases. In particular, we propose a model of fermionic networks that allows us to investigate the network evolution and its dependence on the system temperature. Simulations, performed in accordance with the cited model, clearly highlight the separation between classical random and winnertakesall networks, in full correspondence with the separation between classical and quantum regions for quantum gases. We deem this model useful for the analysis of synthetic and real complex networks.
Categorical quantum mechanics II: Classicalquantum interaction
NASA Astrophysics Data System (ADS)
Coecke, Bob; Kissinger, Aleks
20160801
This is the second part of a threepart overview, in which we derive the categorytheoretic backbone of quantum theory from a process ontology, treating quantum theory as a theory of systems, processes and their interactions. In this part, we focus on classicalquantum interaction. Classical and quantum systems are treated as distinct types, of which the respective behavioral properties are specified in terms of processes and their compositions. In particular, classicality is witnessed by ‘spiders’ which fuse together whenever they connect. We define mixedness and show that pure processes are extremal in the space of all processes, and we define entanglement and show that quantum theory indeed exhibits entanglement. We discuss the classification of tripartite qubit entanglement and show that both the GHZstate and the Wstate come from spiderlike families of processes, which differ only in how they behave when they are connected by two or more wires. We define measurements and provide fully comprehensive descriptions of several quantum protocols involving classical data flow. Finally, we give a notion of ‘genuine quantumness’, from which special processes called ‘phase spiders’ arise, and get a first glimpse of quantum nonlocality.
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.
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
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.
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
Mapping quantumclassical Liouville equation: projectors and trajectories.
Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond
20120228
The evolution of a mixed quantumclassical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantumclassical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectorybased solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.
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 cryptography approaching the classical limit.
Weedbrook, Christian; Pirandola, Stefano; Lloyd, Seth; Ralph, Timothy C
20100910
We consider the security of continuousvariable quantum cryptography as we approach the classical limit, i.e., when the unknown preparation noise at the sender's station becomes significantly noisy or thermal (even by as much as 10(4) times greater than the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptography at wavelengths considerably longer than optical and find that regions of security still exist all the way down to the microwave.
Quantum cryptography approaching the classical limit.
Weedbrook, Christian; Pirandola, Stefano; Lloyd, Seth; Ralph, Timothy C
20100910
We consider the security of continuousvariable quantum cryptography as we approach the classical limit, i.e., when the unknown preparation noise at the sender's station becomes significantly noisy or thermal (even by as much as 10(4) times greater than the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptography at wavelengths considerably longer than optical and find that regions of security still exist all the way down to the microwave. PMID:20867556
Classical system boundaries cannot be determined within quantum Darwinism
NASA Astrophysics Data System (ADS)
Fields, Chris
Multiple observers who interact with environmental encodings of the states of a macroscopic quantum system S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary separating S from its environment E. Quantum Darwinism cannot, therefore, be regarded as providing a purely quantummechanical explanation of the "emergence" of classicality.
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).
Quantumclassical dynamics of wave fields.
Sergi, Alessandro
20070221
An approach to the quantumclassical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled nonlinear equations that can be written by means of a suitable nonHamiltonian bracket. As an example, the theory is applied to the relaxation dynamics of the spinboson model. In the adiabatic limit, a good agreement with calculations performed by the operator approach is obtained. Moreover, the theory proposed in this paper can take nonadiabatic effects into account without resorting to surfacehopping approximations. Hence, the results obtained follow qualitatively those of previous surfacehopping calculations and increase by a factor of (at least) 2, the time length over which nonadiabatic dynamics can be propagated with small statistical errors. Moreover, it is worth to note that the dynamics of quantumclassical wave fields proposed here is a straightforward nonHamiltonian generalization of the formalism for nonlinear quantum mechanics that Weinberg introduced recently.
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.
Classical and quantum physics of hydrogen clusters.
Mezzacapo, Fabio; Boninsegni, Massimo
20090422
We present results of a comprehensive theoretical investigation of the low temperature (T) properties of clusters of parahydrogen (pH(2)), both pristine as well as doped with isotopic impurities (i.e., orthodeuterium, oD(2)). We study clusters comprising up to N = 40 molecules, by means of quantum simulations based on the continuousspace Worm algorithm. Pristine pH(2) clusters are liquidlike and superfluid in the [Formula: see text] limit. The superfluid signal is uniform throughout these clusters; it is underlain by long cycles of permutation of molecules. Clusters with more than 22 molecules display solidlike, essentially classical behavior at temperatures down to T∼1 K; some of them are seen to turn liquidlike at sufficiently low T (quantum melting).
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.
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.
Tomographic quantum cryptography: equivalence of quantum and classical key distillation.
Bruss, Dagmar; Christandl, Matthias; Ekert, Artur; Englert, BertholdGeorg; Kaszlikowski, Dagomir; Macchiavello, Chiara
20030829
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.
Collectibility for mixed quantum states
NASA Astrophysics Data System (ADS)
Rudnicki, Łukasz; Puchała, Zbigniew; Horodecki, Paweł; Życzkowski, Karol
20121201
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for pure states only [Phys. Rev. Lett.PRLTAO0031900710.1103/PhysRevLett.107.150502 107, 150502 (2011)], is extended here for mixed quantum states. We define collectibility for any mixed states of a multipartite system. Deriving bounds for collectibility for positive partially transposed states of given purity provides insight into the structure of entangled quantum states. In the case of two qubits the application of complementary measurements and coincidence based detections leads to a test of entanglement of pseudopure states.
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.
Selected Studies in Classical and Quantum Gravity
NASA Astrophysics Data System (ADS)
Saotome, Ryo
This thesis is composed of two parts, one corresponding to classical and the other to quantum gravitational phenomena. In the classical part, we focus on the behavior of various classical scalar fields in the presence of black holes. New fundamental results discussed include the first confirmation of the Belinskii, Khalatnikov, and Lifschitz (BKL) conjecture for an asymptotically flat spacetime, where we find that the dynamics of a canonical test scalar field near a black hole singularity are dominated by terms with time derivatives. We also perform a numerical simulation of the gravitational collapse of a noncanonical scalar field showing that signals can escape black holes in the kessence dark energy model and find numerical confirmation that the accretion of various scalar fields onto a black hole from generic initial conditions is stationary. In the second part, we focus on the long distance behavior of perturbative quantum gravity. New results discussed include a proof of the cancellation of collinear divergences to all orders in the amplitudes of the theory as well as a characterization of all infrared divergent diagrams. In particular, we find that the only diagrams that can have soft divergences are ladder and crossed ladder diagrams, and that the only collinearly divergent diagrams are those with only three point vertices and no internal jet loops. Also presented is a construction of a double copy relation between gravity and gauge theory amplitudes similar to that conjectured by Bern, Carrasco, and Johansson for the case where there is no hard momentum exchange in the scattering, which we find implies a squaring relation between the classical shockwave solutions of the two theories as well. Finally, the first calculation of a gravitational scattering amplitude through the nexttoleading eikonal order is performed. We find that this correction to the scattering amplitude exponentiates, and that these power corrections probe smaller impact parameters
Kwac, Kijeong; Geva, Eitan
20131121
The effect of vibrational excitation and relaxation of the hydroxyl stretch on the hydrogenbond structure and dynamics of stereoselectively synthesized syntetrol and antitetrol dissolved in deuterated chloroform are investigated via a mixed quantumclassical molecular dynamics simulation. Emphasis is placed on the changes in hydrogenbond structure upon photoexcitation and the nonequilibrium hydrogenbond dynamics that follows the subsequent relaxation from the excited to the ground vibrational state. The propensity to form hydrogen bonds is shown to increase upon photoexcitation of the hydroxyl stretch, thereby leading to a sizable redshift of the infrared emission spectra relative to the corresponding absorption spectra. The vibrational excited state lifetimes are calculated within the framework of Fermi's golden rule and the harmonicSchofield quantum correction factor, and found to be sensitive reporters of the underlying hydrogenbond structure. The energy released during the relaxation from the excited to the ground state is shown to break hydrogen bonds involving the relaxing hydroxyl. The spectral signature of this nonequilibrium relaxation process is analyzed in detail.
Quantum information theory: classical communication over quantum channels
NASA Astrophysics Data System (ADS)
Cortese, John Anthony
This thesis studies classical communication over quantum channels. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their Bloch vectors. The application of the Bloch vector relative entropy formula to the determination of HolevoSchumacherWestmoreland (HSW) capacities for qubit quantum channels is discussed. Chapter 3 outlines several numerical simulation results which support theoretical conclusions and conjectures discussed in Chapters 1 and 2. Chapter 4 closes the thesis with comments, examples and discussion on the additivity of Holevo Chi and the HSW channel capacity.
The scalable implementation of quantum walks using classical light
NASA Astrophysics Data System (ADS)
Goyal, Sandeep K.; Roux, F. S.; Forbes, Andrew; Konrad, Thomas
20140201
A quantum walk is the quantum analog of the classical random walks. Despite their simple structure they form a universal platform to implement any algorithm of quantum computation. However, it is very hard to realize quantum walks with a sufficient number of iterations in quantum systems due to their sensitivity to environmental influences and subsequent loss of coherence. Here we present a scalable implementation scheme for onedimensional quantum walks for arbitrary number of steps using the orbital angular momentum modes of classical light beams. Furthermore, we show that using the same setup with a minor adjustment we can also realize electric quantum walks.
Emergence of a classical Universe from quantum gravity and cosmology.
Kiefer, Claus
20120928
I describe how we can understand the classical appearance of our world from a universal quantum theory. The essential ingredient is the process of decoherence. I start with a general discussion in ordinary quantum theory and then turn to quantum gravity and quantum cosmology. There is a whole hierarchy of classicality from the global gravitational field to the fluctuations in the cosmic microwave background, which serve as the seeds for the structure in the Universe.
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.
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.
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
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.
Comparisons of classical and quantum dynamics for initially localized states
Davis, M.J.; Heller, E.J.
19840515
We compare the dynamics of quantum wave packets with the dynamics of classical trajectory ensembles. The wave packets are Gaussian with expectation values of position and momenta which centers them in phase space. The classical trajectory ensembles are generated directly from the quantum wave packets via the Wigner transform. Quantum and classical dynamics are then compared using several quantum measures and the analogous classical ones derived from the Wigner equivalent formalism. Comparisons are made for several model potentials and it is found that there is generally excellent classicalquantum correspondence except for certain specific cases of tunneling and interference. In general, this correspondence is also very good in regions of phase space where there is classical chaos.
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.
Ergodicity and mixing in quantum dynamics
NASA Astrophysics Data System (ADS)
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.
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
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.
Extended hydrodynamic approach to quantumclassical nonequilibrium evolution. I. Theory.
Bousquet, David; Hughes, Keith H; Micha, David A; Burghardt, Irene
20110214
A mixed quantumclassical formulation is developed for a quantum subsystem in strong interaction with an Nparticle environment, to be treated as classical in the framework of a hydrodynamic representation. Starting from the quantum Liouville equation for the Nparticle distribution and the corresponding reduced singleparticle distribution, exact quantum hydrodynamic equations are obtained for the momentum moments of the singleparticle distribution coupled to a discretized quantum subsystem. The quantumclassical limit is subsequently taken and the resulting hierarchy of equations is further approximated by various closure schemes. These include, in particular, (i) a GradHermitetype closure, (ii) a Gaussian closure at the level of a quantumclassical local Maxwellian distribution, and (iii) a dynamical density functional theory approximation by which the hydrodynamic pressure term is replaced by a free energy functional derivative. The latter limit yields a mixed quantumclassical formulation which has previously been introduced by I. Burghardt and B. Bagchi, Chem. Phys. 134, 343 (2006).
Quantum Particles from Classical Probabilities in Phase Space
NASA Astrophysics Data System (ADS)
Wetterich, C.
20121001
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow, including interference or tunneling. The appropriate quantum observables for position and momentum contain a statistical part which reflects the roughness of the probability distribution. "Zwitters" realize a continuous interpolation between quantum and classical particles. Such objects may provide for an effective oneparticle description of classical or quantum collective states as droplets of a liquid, macromolecules or a BoseEinstein condensate. They may also be used for quantitative fundamental tests of quantum mechanics. We show that the ground state for zwitters has no longer a sharp energy. This feature permits to put quantitative experimental bounds on a small parameter for possible deviations from quantum mechanics.
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.
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; Zurek, Wojciech H.
20130101
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. We also 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. The resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.
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.
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.
Hybrid QuantumClassical Approach to Correlated Materials
NASA Astrophysics Data System (ADS)
Bauer, Bela; Wecker, Dave; Millis, Andrew J.; Hastings, Matthew B.; Troyer, Matthias
20160701
Recent improvements in the control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantumclassical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is selfconsistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around 100 logical qubits becomes available.
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.
Hybrid quantumclassical approach to correlated materials
NASA Astrophysics Data System (ADS)
Bauer, Bela; Wecker, Dave; Millis, Andrew J.; Hastings, Matthew B.; Troyer, Matthias
Recent improvements in control of quantum systems make it seem feasible to finally build a programmable generalpurpose quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantumclassical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is selfconsistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around one hundred logical qubits becomes available.
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
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.
Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades.
Yepez, Jeffrey; Vahala, George; Vahala, Linda; Soe, Min
20090821
The main topological feature of a superfluid is a quantum vortex with an identifiable inner and outer radius. A novel unitary quantum lattice gas algorithm is used to simulate quantum turbulence of a BoseEinstein condensate superfluid described by the GrossPitaevskii equation on grids up to 5760(3). For the first time, an accurate powerlaw scaling for the quantum Kelvin wave cascade is determined: k(3). The incompressible kinetic energy spectrum exhibits very distinct powerlaw spectra in 3 ranges of k space: a classical Kolmogorov k((5/3)) spectrum at scales greater than the outer radius of individual quantum vortex cores and a quantum Kelvin wave cascade spectrum k(3) on scales smaller than the inner radius of the quantum vortex core. The k(3) quantum Kelvin wave spectrum due to phonon radiation is robust, while the k((5/3)) classical Kolmogorov spectrum becomes robust on large grids.
Quantum and classical simulations of molecular clusters
NASA Astrophysics Data System (ADS)
Dong, Xiao
to a fast discovery of accessible topological paths towards the global minimum. The ATMC can be readily linked to systems described by classical model potentials or systems described quantum mechanically. Serial and parallel versions of the ATMC have been implemented and applied for the structural optimization of classical LennardJones nanoclusters and Morse nanoclusters, and tightbinding calcium nanoclusters, crystallization of infinite LennardJones liquid, and optimization of the folding process leading to the native state of a polypeptide chain.
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.
Hybrid quantum/classical approaches for proton transfer in condensed phase systems
NASA Astrophysics Data System (ADS)
Kim, Soo Young
Nuclear quantum effects such as tunneling and zero point energy play an important role in proton transfer reactions. Since a fully quantum mechanical treatment of condensed phase systems is not practical, mixed quantum/classical methods have been developed to simulate proton transfer reactions in solution. In this work the molecular dynamics with quantum transitions (MDQT) method, which incorporates nonadiabatic transitions among the vibrational states, was extended to treat the donoracceptor vibrational motion as well as the hydrogen motion quantum mechanically for proton transfer reactions. This approach was applied to a model system representing intramolecular proton transfer within a phenolamine complex in liquid methyl chloride. In addition, a hybrid quantum/classical molecular dynamics approach was applied to a proton transfer reaction represented by a symmetric double well system coupled to a dissipative bath. The hybrid quantum/classical results agree well with numerically exact results in the spatialdiffusionlimited regime, which is most relevant for proton transfer in proteins. In these two studies, the fundamental issues such as the nuclear quantum effects of the proton and donoracceptor motions and the dissipation effects in the hybrid quantum/classical approach were explored. These results have important implications for applications to hydrogen transfer reactions in solution and proteins.
Generic emergence of classical features in quantum Darwinism
NASA Astrophysics Data System (ADS)
Brandão, Fernando G. S. L.; Piani, Marco; Horodecki, Paweł
20150801
Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a systemofinterest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations.
Generic emergence of classical features in quantum Darwinism.
Brandão, Fernando G S L; Piani, Marco; Horodecki, Paweł
20150101
Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a systemofinterest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations.
Controlling the dynamics of classical and quantum information in spin systems
NASA Astrophysics Data System (ADS)
Dalal, Parin B.
The precise, human control of quantum systems, by its definition, must combine models of the classical and the quantum world into a calculus that supports both. Open, irreversible quantum systems must interact with closed, reversible quantum systems to predict evolutions that are partially open and closed. Inevitably, the problems of quantum measurement, the assumptions of scattering, and the role of spacetime comes under scrutiny. Such considerations have extraordinary practical value: the precise control of a quantum information is the cornerstone of scalable quantum computing. Traditionally, quantum control theory as well as a formalism of redundancy and partial measurements, known as quantum error correction, attempt to remedy systematic quantumnoise and random quantumnoise respectively, but have had mixed success. This dissertation examines how the imprecision of control in quantum and classical spin systems affects the flow of select information to a receiver and how such systems may be optimized against the imprecise scattering of control fields and spins. To this end, this dissertation intertwines the physics of state evolution with the physics of information control in classical and quantum systems. First in classical systems, a method for encoding and decoding classical spinprocessing information provides an example of information flow. Then an analytic calculation of a semiconductor spin channel's information capacity is performed. The results limit the rate of information processing and inform the design of materials for optimal spintronic informationprocessing in semiconductors. Next, noisy quantum interactions are described, so that the complexities of correcting small, random phase errors using traditional control theory and quantum error correction may be explained. How these noisy processes affect the relevant information flow of a quantum algorithm (derivatives of the Quantum Fourier Transform and Grover Search) is considered, several novel
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.
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
Inverse Problems in Classical and Quantum Physics
NASA Astrophysics Data System (ADS)
Almasy, Andrea A.
20091201
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from taudecay data and the inverse conductivity problem. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the timelike experimental data with asymptotic spacelike results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. In this thesis, also two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the crosssection of a human chest. Even though the human volunteer is neither twodimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.
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).
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.
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.
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
Classical and quantum dynamics of the impulsively driven hydrogen atom
Melles, M.; Reinhold, C.O.; Burgdoerfer, J. 
19921201
We investigate the classical and quantum dynamics of the hydrogen atom in a Rydberg state subject to a sequence of periodic and random pulses. One goal of this study is to test the validity of classical electron transport theories. We analyze the critical momentum transfer for which 10% of the Rydberg atoms are ionized after a large number of pulses as a function of the frequency of the perturbation. The quantum mechanical results for a periodic sequence of pulses exhibit clear structures which are not present in a classical simulation. These structures are shown to vanish for the case of stochastic pulses for which agreement is obtained between the classical and quantum mechanical results. The dynamics of the quantum mechanical periodic system is analyzed in terms of quasieigenstates of the periodone time evolution operator.
Strongfield ionization in classical and quantum dynamics
Ritchie, B. ); Bowden, C.M.; Sung, C.C.; Li, Y.Q. )
19900601
Classical and quantum results for the strongelectromagneticfield ionization of the ground state of a generic model are compared. Quantum results are also presented for the strongfield ionization of the hydrogen atom. These results demonstrate that ionization depends strongly on the phase of the field in such a way that the interaction potential acts as a barrier or well at large distances from the binding region, producing effectively a closed or open gate'' to the region of space outside the atom. The open gate is analogous to a strong, static electric field applied to an atom such that the atom ionizes classically. Quantum and classical ensemble results for the ionization probability are found to show close qualitative agreement. Other comparisons are made for classical versus quantum wavepacket trajectories.
Classical and quantum dynamics of the impulsively driven hydrogen atom
Melles, M.; Reinhold, C.O.; Burgdoerfer, J. Oak Ridge National Lab., TN )
19920101
We investigate the classical and quantum dynamics of the hydrogen atom in a Rydberg state subject to a sequence of periodic and random pulses. One goal of this study is to test the validity of classical electron transport theories. We analyze the critical momentum transfer for which 10% of the Rydberg atoms are ionized after a large number of pulses as a function of the frequency of the perturbation. The quantum mechanical results for a periodic sequence of pulses exhibit clear structures which are not present in a classical simulation. These structures are shown to vanish for the case of stochastic pulses for which agreement is obtained between the classical and quantum mechanical results. The dynamics of the quantum mechanical periodic system is analyzed in terms of quasieigenstates of the periodone time evolution operator.
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.
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 Schroedinger 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
Experimental characterization of Gaussian quantum discord generated by fourwave mixing
NASA Astrophysics Data System (ADS)
Vogl, Ulrich; Glasser, Ryan T.; Glorieux, Quentin; Clark, Jeremy B.; Corzo, Neil V.; Lett, Paul D.
20130101
We experimentally determine the Gaussian quantum discord present in twomode squeezed vacuum generated by a fourwave mixing process in hot rubidium vapor. The frequency spectra of the discord as well as the quantum and classical mutual information are also measured. In addition, the effects of symmetric attenuation introduced into both modes of the squeezed vacuum on the Gaussian quantum discord, and the quantum mutual information and the classical correlations are examined experimentally. Finally, we show that due to the multispatialmode nature of the fourwave mixing process, the Gaussian quantum discord may exhibit sub or superadditivity depending on which spatial channels are selected.
Playing with functions of positive type, classical and quantum
NASA Astrophysics Data System (ADS)
Aniello, Paolo
20150601
A function of positive type can be defined as a positive functional on a convolution algebra of a locally compact group. In the case where the group is abelian, by Bochner’s theorem a function of positive type is, up to normalization, the Fourier transform of a probability measure. Therefore, considering the group of translations on phase space, a suitably normalized phasespace function of positive type can be regarded as a realization of a classical state. Thus, it may be called a function of classical positive type. Replacing the ordinary convolution on phase space with the twisted convolution, one obtains a noncommutative algebra of functions whose positive functionals we may call functions of quantum positive type. In fact, by a quantum version of Bochner’s theorem, a continuous function of quantum positive type is, up to normalization, the (symplectic) Fourier transform of a Wigner quasiprobability distribution; hence, it can be regarded as a phasespace realization of a quantum state. Playing with functions of positive type—classical and quantum—one is led in a natural way to consider a class of semigroups of operators, the classicalquantum semigroups. The physical meaning of these mathematical objects is unveiled via quantization, so obtaining a class of quantum dynamical semigroups that, borrowing terminology from quantum information science, may be called classicalnoise semigroups.
Experimental detection of nonclassical correlations in mixedstate quantum computation
Passante, G.; Moussa, O.; Trottier, D. A.; Laflamme, R.
20111015
We report on an experiment to detect nonclassical correlations in a highly mixed state. The correlations are characterized by the quantum discord and are observed using four qubits in a liquidstate nuclear magnetic resonance quantum information processor. The state analyzed is the output of a DQC1 computation, whose input is a single quantum bit accompanied by n maximally mixed qubits. This model of computation outperforms the best known classical algorithms and, although it contains vanishing entanglement, it is known to have quantum correlations characterized by the quantum discord. This experiment detects nonvanishing quantum discord, ensuring the existence of nonclassical correlations as measured by the quantum discord.
Classical and quantum communication without a shared reference frame.
Bartlett, Stephen D; Rudolph, Terry; Spekkens, Robert W
20030711
We show that communication without a shared reference frame is possible using entangled states. Both classical and quantum information can be communicated with perfect fidelity without a shared reference frame at a rate that asymptotically approaches one classical bit or one encoded qubit per transmitted qubit. We present an optical scheme to communicate classical bits without a shared reference frame using entangled photon pairs and linear optical Bell state measurements.
Comparison of quantum and classical relaxation in spin dynamics.
Wieser, R
20130401
The classical LandauLifshitz equation with a damping term has been derived from the time evolution of a quantum mechanical wave function under the assumption of a nonHermitian Hamilton operator. Further, the trajectory of a classical spin (S) has been compared with the expectation value of the spin operator (Ŝ). A good agreement between classical and quantum mechanical trajectories can be found for Hamiltonians linear in Ŝ or S, respectively. Quadratic or higher order terms in the Hamiltonian result in a disagreement.
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.
Nonmonotonicity in the quantumclassical transition: chaos induced by quantum effects.
Kapulkin, Arie; Pattanayak, Arjendu K
20080815
The classicalquantum transition for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative variant Planck's over 2pi is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the doublewell Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective variant Planck's over 2pi is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantumclassical transition in this case is nonmonotonic in variant Planck's over 2pi. PMID:18764537
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
