Supersymmetry versus integrability in two-dimensional classical mechanics

Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of the constants of motion is unveiled and the entanglement between integrability and supersymmetry is explored.     

Quantum and classical correlations in a classical dephasing environment

We calculate the non-Markovian dynamics of quantum correlations, including entanglement and discord, and classical correlation in a two-qubit system with Ornstein-Uhlenbeck noise and discuss the relations in these correlations. It?s found that the initial-state parameters and the non-Markovian properties play an important role in these dynamics behaviors.     

On the inverse FPR problem: Quantum is classical

The notion of quantum supports introduced by Foulis, Piron, and Randall can be used to construct combinatorial versions of contextualist hidden-variable models for finite quantum logics. The original logic can be uniquely recovered from appropriate such models as a solution of a combinatorial inverse problem. One can thus set up a classical ontology for a finite quantum logics that completely specifies it. Computer studies are used to explore the ideas.     

Quantum reading of a classical digital memory

We consider a basic model of digital memory where each cell is composed of a reflecting medium with two possible reflectivities. By fixing the mean number of photons irradiated over each memory cell, we show that a nonclassical source of light can retrieve more information than any classical source. This improvement is shown in the regime of few photons and high reflectivities, where the gain of information can be surprising. As a result, the use of quantum light can have nontrivial applications in the technology of digital memories, such as optical disks and barcodes.     

Limit on nonlocality in any world in which communication complexity is not trivial

Bell proved that quantum entanglement enables two spacelike separated parties to exhibit classically impossible correlations. Even though these correlations are stronger than anything classically achievable, they cannot be harnessed to make instantaneous (faster than light) communication possible. Yet, Popescu and Rohrlich have shown that even stronger correlations can be defined, under which instantaneous communication remains impossible. This raises the question: Why are the correlations achievable by quantum mechanics not maximal among those that preserve causality? We give a partial answer to this question by showing that slightly stronger correlations would result in a world in which communication complexity becomes trivial.     

Quantum mechanics as a classical diffusion process

A direct construction is provided showing that the classical expectation value for the energy of a particle executing a classical diffusion process is equivalent to the quantum mechanical form with a Hamiltonian structured like that for a charged particle in an electromagnetic field.     

On the integrability of classical spinor models in two-dimensional space-time

Well known classical spinor relativistic-invariant two-dimensional field theory models, including the Gross-Neveu, Vaks-Larkin-Nambu-Jona-Lasinio and some other models, are shown to be integrable by means of the inverse scattering problem method. These models are shown to be naturally connected with the principal chiral fields on the symplectic, unitary and orthogonal Lie groups. The respective technique for construction of the soliton-like solutions is developed.     

Quantum NOT operation and integrability in two-level systems

We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different “average” systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally, we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps.     

Quantum mechanics as a deformation of classical mechanics

Mathematical properties of deformations of the Poisson Lie algebra and of the associative algebra of functions on a symplectic manifold are given. The suggestion to develop quantum mechanics in terms of these deformations is confronted with the mathematical structure of the latter. As examples, spectral properties of the harmonic oscillator and of the hydrogen atom are derived within the new formulation. Further mathematical generalizations and physical applications are proposed.Work supported in part by the National Science Foundation.     

量子保密通讯及经典密码

密码技术的发展经历了古典密码、现代密码和量子密钥分发三个阶段。首颗量子卫星“墨子号”的成功发射,使量子密钥分发技术迈向新里程。文章介绍了密码发展的各个进程,并详细介绍了目前广泛应用的RSA公钥密码系统,以及量子密钥分发使用的BB84协议,E91协议等。文末简要介绍了量子保密通信进展,并对“墨子号”量子科学实验卫星实验任务及重要意义做出解读。     

Nonstationary quantum mechanics. III. Quantum mechanics does not incorporate classical physics

It is shown that disagreement between the prediction of classical and conventional quantum mechanics about momentum probabilities exists in the case of a quasiclassical motion. The discussion is based on the detailed consideration of two specific potentials:U(x)=x and the oscillatory potentialU(x)=m ² x ²/2. The results of the present Part III represent a further development of the idea in Todorov (1980) about the possible inefficiency of conventional theory in the case of potentials swiftly varying with time.     

Quantum mechanics in a discrete model of classical physics

The role of probability theory in classical physics is examined. It is found that the probabilities for the outcomes of typical experiments depend strongly on the assumed behavior of given classical models at infinity. A discrete classical model is introduced and it is shown that the resulting probabilities are similar to those in the usual theory of quantum mechanics.     

Quantum particles and classical particles

The relation between wave mechanics and classical mechanics is reviewed, and it is stressed that the latter cannot be regarded as the limit of the former as 0. The motion of a classical particle (or ensemble of particles) is described by means of a Schrödinger-like equation that was found previously. A system of a quantum particle and a classical particle is investigated (1) for an interaction that leads to stationary states with discrete energies and (2) for an interaction that enables the classical particle to act as a measuring instrument for determining a physical variable of the quantum particle.     

Quantum particles from classical statistics

Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being “classical” or “quantum” ceases to be a basic conceptual difference. The dynamics differs, however, between quantum and classical particles. We describe position, motion and correlations of a quantum particle in terms of observables in a classical statistical ensemble. On the other side, we also construct explicitly the quantum formalism with wave function and Hamiltonian for classical particles. For a suitable time evolution of the classical probabilities and a suitable choice of observables all features of a quantum particle in a potential can be derived from classical statistics, including interference and tunneling. Besides conceptual advances, the treatment of classical and quantum particles in a common formalism could lead to interesting cross‐fertilization between classical statistics and quantum physics.