We propose a Wigner function based parameter that can be used as an indicator of quantum chaos. This parameter is defined as "entropy" from the time-dependence of "non-classicallity" proposed in \cite{KZ04}. We perform our considerations for the system of damped nonlinear (Kerr-like) oscillator excited by a series of ultra-short external pulses.
A fluid analog of the information flux in the phase-space associated to purity and von Neumann entropy are identified in the Weyl-Wigner formalism of quantum mechanics. Once constrained by symmetry and positiveness, the encountered continuity equations provide novel quantifiers for non-classicality (non-Liouvillian fluidity) given in terms of quantum decoherence, purity and von Neumann entropy fluxes. Through definitions in the Weyl-Wigner formalism, one can identify the quantum fluctuations that distort the classical-quantum coincidence regime, and the corresponding quantum information profil…
Phase-space features of the Wigner flow for an anharmonic quantum system driven by the harmonic oscillator potential modified by the addition of an inverse square (one-dimension Coulomb-like) contribution are analytically described in terms of Wigner functions and Wigner currents. Reporting about three correlated continuity equations which quantify the flux of quantum information in the phase-space, the non-classicality profile of such an anharmonic system can be consistently obtained in terms of the fluxes of {\em probability}, {\em purity} and {\em von Neumann-like entropy}. Considering that…
In the report we analyze the indicator/measure of classicality of quantum states defined as the probability to find a state with a positive Wigner function within a unitary invariant random ensemble. The indicators of classicality of three ensembles associated with the Hilbert-Schmidt, Bures and Bogoliubov-Kubo-Mori metrics on the space of quantum states of 3-level system are computed. Their dependence on a moduli parameter of the Wigner function is studied for all strata of a qutrit state space stratified in accordance with the unitary group action.
One of the central foundational questions of physics is to identify what makes a system quantum as opposed to classical. One seminal notion of classicality of a quantum system is the existence of a non-contextual hidden variable model as introduced in the early work by Bell, Kochen and Specker. In quantum optics, the non-negativity of the Wigner function is a ubiquitous notion of classicality. In this work we establish an equivalence between these two concepts. In particular, we show that any non-contextual hidden variable model for Gaussian quantum optics has an alternative non-negative Wigne…
In this report we are aiming at introducing a global measure of non-classicality of the state space of $N$-level quantum systems and estimating it in the limit of large $N$. For this purpose we employ the Wigner function negativity as a non-classicality criteria. Thus, the specific volume of the support of negative values of Wigner function is treated as a measure of non-classicality of an individual state. Assuming that the states of an $N$-level quantum system are distributed by Hilbert-Schmidt measure (Hilbert-Schmidt ensemble), we define the global measure as the average non-classicality o…
It is commonly accepted that a deviation of the Wigner quasiprobability distribution of a quantum state from a proper statistical distribution signifies its nonclassicality. Following this ideology, we introduce the global indicator $\mathcal{Q}_N$ for quantification of "classicality-quantumness" correspondence in the form of the functional on the orbit space $\mathcal{O}[\mathfrak{P}_N]$ of the $SU(N)$ group adjoint action on the state space $\mathfrak{P}_N$ of an $N$-dimensional quantum system. The indicator $\mathcal{Q}_{N}$ is defined as a relative volume of a subspace $\mathcal{O}[\mathfr…
Loschmidt Echo and Classicality of the Gamma Model
Escola Agrotécnica da Universidade Federal de Roraima（罗赖马联邦大学农业技术学校）；Departamento de Física e Matemática, Universidade Federal de São João Del Rei（圣若昂德尔雷伊联邦大学物理与数学系）
In the present report we discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions. Particularly, the dependence of the global indicator of classicality on the assigned geometry of a quantum state space is analysed for a whole family of Wigner quasiprobability representations. General considerations are exemplified by constructing the global indicator of classicality/quantumness for the Hilbert-Schmidt, Bures and Bogoliubov-Kubo-Mori ensembles of qubits and q…
Banaszek, Wódkiewicz and others (\cite{Banaszek},\cite{Chen},\cite{Chen-Zhang}) made the surprising discovery that Einstein-Bell locality inequalities can be violated by the two mode squeezed vacuum by a factor $\sqrt{2}$, in spite of the fact that the state has a positive Wigner function. I use here the more general Gleason-Kochen-Specker assumption of non-contextuality \cite{Gleason} to express classicality. I then derive non-contextuality Bell inequalities for correlations of $N$ pseudo spins embedded in an infinite dimensional continuous variable Hilbert space, and show that their maximum …
In this paper, We investigate three-mode photon-added Greenberger-Horne-Zeilinger (GHZ) entangled coherent states by repeatedly operating the photon-added operator on the GHZ entangled coherent states. The product of two Laguerre polynomials is demonstrated to be connected to the normalizing constant. The influence of the operation on the non-classical and non-Gaussian behavior of the GHZ entangled coherent states is investigated. Sub-Poissonian statistics, such as Mandel's parameter and the negativity of the Wigner function, show that non-classical properties can enhance GHZ entangled coheren…
In this note, we consider the question of classicality for the theory which is known to be the effective description of two-dimensional black holes - the Morse quantum mechanics. We calculate the Wigner function and the Fisher information characterizing classicality/quantumness of single-particle systems and briefly discuss further directions to study.
The spin-$j$ Einstein-Podolsky-Rosen experiment is studied with a view to understanding how classical behaviour emerges as $j \to \infty$. It is proposed that it is necessary to include detector error, which if it is be to viewed as an essential aspect of the emergence of classicality, should be both minimal, i.e., no more than necessary to wash out quantum mechanical behaviour, and agnostic, by which is meant that one should be able to ascribe it to error in the preparation of the state just as well as to the detector.Errors in the state preparation are discussed via the spin Wigner function.…
Emergent classicality and wavefunction branching in an isolated quantum many-body system
Center for Theoretical Physics — a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心）；Harvard University（哈佛大学）；California Institute of Technology（加州理工学院）；NTT Research, Inc.（日本电报电话公司研究所）
For the visualization of quantum states, the approach based on Wigner functions can be very effective. Homodyne detection has been extensively used to obtain the density matrix, Wigner functions and tomographic reconstructions of optical fields for many thermal, coherent or squeezed states. Here, we use time-domain optical homodyne tomography for the quantum state recognition and reconstruction of the femtosecond optical field from a nonequilibrium superradiant coherent electron-hole state formed in a semiconductor laser structure. We observe severe deviations from the Poissonian statistics of…
Gravitational Entanglement in Optomechanics: Distinguishing Classical and Quantum Models
University of Vienna（维也纳大学）；Technion – Israel Institute of Technology（以色列理工学院）；Xiamen University Malaysia（马来西亚厦门大学）；University of Gdańsk（格但斯克大学）；Indian Institute of Technology Roorkee（印度理工学院罗尔基分校）；Austrian Academy of Sciences（奥地利科学院）
In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behaviour in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numericall…
By means of studying the evolution equation for the Wigner distributions of quantum dissipative systems we derive the quantum corrections to the classical Liouville dynamics, taking into account the standard quantum friction model. The resulting evolution turns out to be the classical one plus fluctuations that depend not only on the $\hbar$ size but also on the momentum and the dissipation parameter (i.e. the coupling with the environment). On the other hand, we extend our studies of a paradigmatic system based on the kicked rotator, and we confirm that by adding fluctuations only depending o…
We study the classical chaos appearing in a diatomic molecules $BeO$, $CO$ and $CN$ due to the interaction with a circularly polarized electric field, and its signature in Quantum Mechanics through the Wigner distribution function and the Boltzmann-Shannon entropy. We found a motion out of the center of the quantum phase space defined by Wigner function when the classical system becomes chaotic, and we found a jumping behavior of the average Boltzmann-Shannon entropy with respect the electric field strength when the classical system becomes chaotic, indicating a sudden increasing in the disord…
Although highly successful, the Truncated Wigner Approximation (TWA) does not account for genuine many-body quantum interference between different solutions of the mean-field equations of a bosonic many-body (MB) system. This renders the TWA essentially classical, where a large number of particles formally takes the role of the inverse of Planck's constant $\hbar$. The failure to describe genuine interference phenomena, such as localization and scarring in Fock space, can be seen as a virtue of this quasiclassical method, which thereby allows one to identify genuine quantum effects when being …
We experimentally reconstruct Wigner's current of quantum phase space dynamics for the first time. We reveal the ``push-and-pull" associated with damping and diffusion due to the coupling of a squeezed vacuum state to its environment. In contrast to classical dynamics, where (at zero temperature) dissipation only ``pulls" the system toward the origin of phase space, we also observe an outward ``push" because our system has to obey Heisenberg's uncertainty relations. With squeezed vacuum states generated by an optical parametric oscillator at variable pumping levels, we identify the pure squeez…
We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the $\mathcal{L}^2 (\R^2)$ distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [0,1], being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number o…
