Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0801.3003 · Physical Review A

Quantum-classical correspondence in entanglement production: Entropy and classical tori

Shihui Zhang, Quanlin Jie

Published Jan 14, 2008• 18 citations
arXivHTMLPDF

Abstract

We analyze the connections between entanglement dynamics and classical trajectories in a semiclassical regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on classical invariant tori and such phenomenon is closely related to the power spectra of classical trajectories. Classical power spectrum with a larger number of frequency components corresponds to larger entanglement. We introduce a frequency entropy to describe the classical frequency distribution. It is found that there is good correspondence between the classical frequency entropies and the maximum von Neumann entropies.

DOI
10.1103/physreva.77.012312

Related papers

Quantum-Classical Correspondence in Entanglement Production of the Spin System:Entanglement and Classical Frequency Entropy

Jie Quan-Lin

This paper is devoted to analyzing the connections between entanglement dynamics and classical trajectories with a model of coupled rotor.In the numerical simulation of quantum evolution and the frequency spectrum analysis of classical orbit,we find that entanglement production depends on classical orbit and such phenomenon is closely related to the power spectra of classical trajectories.Classical power spectrum with a more complicated structure corresponds to faster entanglement.With the classical power spectrum,we introduce a new quantity,i.e.,the frequency entropy,to measure the stability of classical orbit.The results show that there is good correspondence between the classical frequency entropies and the maximum von Neumann entropies.

Journal of Wuhan University•Jan 1, 2009•0 citations

Entanglement dynamics and classical frequency spectrum in an integrable system

Shihui Zhang, Qing Wu Wang, Hongbao Liu

The role of classical dynamics in entanglement production for an integrable system is analyzed with a model of two coupled oscillators. It is found that the entanglement of an intergrable system is closely connected with the frequency of classical motion. For different classical orbits, the entanglement of the system increases with the classical frequency entropy, which can reveal the frequency spectrum of the classical motion.

Symposium on ICT and Energy Efficiency and Workshop on Information Theory and Security (CIICT)•Jan 1, 2012•0 citations

Dependence of entanglement dynamics on the global classical dynamical regime

Ning Ning Chung, Lock Yue Chew

We analyze the connections between the dynamical generation of continuous variable entanglement and the underlying classical trajectories in pairs of coupled oscillators. In the quantization of a periodic cycle, we find periodic entanglement which has twice the frequency of the corresponding classical motion. Such frequency doubling continues to hold true in the entanglement dynamics for a second model that exhibits a two-frequency orbit in the classical domain. In addition, the periodicity and the quasiperiodicity of the entanglement are found to be independent of the local classical dynamical behavior. Finally, in our third model, the entanglement production rate is found to be (i) higher in the chaotic regime and (ii) insensitive toward the choice of regular or chaotic initial condition in the mixed regime. In summary, we have illustrated through our sample models that the generation of dynamical pattern of entanglement can depend completely on the global classical dynamical regime without being influenced by the local classical behavior.

Physical Review E•Jul 7, 2009•24 citations

Quantum–Classical Entropy Analysis for Nonlinearly-Coupled Continuous-Variable Bipartite Systems

Ángel S. Sanz

The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space-a common meeting point to both classical and quantum density statistical descriptors. Here, this issue is tackled by investigating the behavior of classical analogs arising upon the removal of all interference traits displayed by the Wigner distribution functions associated with a given pure quantum state. Accordingly, the dynamical evolution of the linear and von Neumann entropies is numerically computed for a continuous-variable bipartite system, and compared with the corresponding classical counterparts, in the case of two quartic oscillators nonlinearly coupled under regular and chaos conditions. Three quantum states for the full system are considered: a Gaussian state, a cat state, and a Bell-type state. By comparing the quantum and classical entropy values, and particularly their trends, it is shown that, instead of entanglement production, such entropies rather provide us with information on the system (either quantum or classical) delocalization. This gradual loss of information translates into an increase in both the quantum and the classical realms, directly connected to the increase in the correlations between both parties' degrees of freedom which, in the quantum case, is commonly related to the production of entanglement.

arXiv:2111.10165•Entropy•Jan 27, 2022•3 citations

Relationship between the linear entropy, the von Neumann entropy and the atomic Wehrl entropy for the Jaynes-Cummings model

Faisal A. A. El-Orany

The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations.

arXiv:0705.4373•May 30, 2007•2 citations

Entanglement dynamics via coherent-state propagators

A. D. Ribeiro, R. M. Angelo

The dynamical generation of entanglement in closed bipartite systems is investigated in the semiclassical regime. We consider a model of two particles, initially prepared in a product of coherent states, evolving in time according to a generic Hamiltonian, and derive a formula for the linear entropy of the reduced density matrix using the semiclassical propagator in the coherent-state representation. The formula is explicitly written in terms of quantities that define the stability of classical trajectories of the underlying classical system. The formalism is then applied to the problem of two nonlinearly coupled harmonic oscillators, and the result is shown to be in remarkable agreement with the exact quantum measure of entanglement in the short-time regime. An important by-product of our approach is a unified semiclassical formula, which contemplates both the coherent-state propagator and its complex conjugate.

arXiv:1009.2079•Physical Review A•Nov 29, 2010•13 citations
We analyze the connections between entanglement dynamics and classical trajectories in a semiclassical regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on classical invariant tori and such phenomenon is closely related to the power spectra of classical trajectories. Classical power spectrum with a larger number of frequency components corresponds to larger entanglement. We introduce a frequency entropy to describe the classical frequency distribution. It is found that there is good correspondence between the classical frequency entropies and the maximum von Neumann entropies.
This paper is devoted to analyzing the connections between entanglement dynamics and classical trajectories with a model of coupled rotor.In the numerical simulation of quantum evolution and the frequency spectrum analysis of classical orbit,we find that entanglement production depends on classical orbit and such phenomenon is closely related to the power spectra of classical trajectories.Classical power spectrum with a more complicated structure corresponds to faster entanglement.With the classical power spectrum,we introduce a new quantity,i.e.,the frequency entropy,to measure the stability of classical orbit.The results show that there is good correspondence between the classical frequency entropies and the maximum von Neumann entropies.
We analyze the connections between the dynamical generation of continuous variable entanglement and the underlying classical trajectories in pairs of coupled oscillators. In the quantization of a periodic cycle, we find periodic entanglement which has twice the frequency of the corresponding classical motion. Such frequency doubling continues to hold true in the entanglement dynamics for a second model that exhibits a two-frequency orbit in the classical domain. In addition, the periodicity and the quasiperiodicity of the entanglement are found to be independent of the local classical dynamical behavior. Finally, in our third model, the entanglement production rate is found to be (i) higher in the chaotic regime and (ii) insensitive toward the choice of regular or chaotic initial condition in the mixed regime. In summary, we have illustrated through our sample models that the generation of dynamical pattern of entanglement can depend completely on the global classical dynamical regime without being influenced by the local classical behavior.
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space-a common meeting point to both classical and quantum density statistical descriptors. Here, this issue is tackled by investigating the behavior of classical analogs arising upon the removal of all interference traits displayed by the Wigner distribution functions associated with a given pure quantum state. Accordingly, the dynamical evolution of the linear and von Neumann entropies is numerically computed for a continuous-variable bipartite system, and compared with the corresponding classical counterparts, in the case of two quartic oscillators nonlinearly coupled under regular and chaos conditions. Three quantum states for the full system are considered: a Gaussian state, a cat state, and a Bell-type state. By comparing the quantum and classical entropy values, and particularly their trends, it is shown that, instead of entanglement production, such entropies rather provide us with information on the system (either quantum or classical) delocalization. This gradual loss of information translates into an increase in both the quantum and the classical realms, directly connected to the increase in the correlations between both parties' degrees of freedom which, in the quantum case, is commonly related to the production of entanglement.
The linear entropy, the von Neumann entropy and the atomic Wehrl entropy are frequently used to quantify entanglement in the quantum systems. These relations provide typical information on the entanglement in the Jaynes-Cummings model (JCM). In this Letter, we explain the origin of this analytically and derive a closed form for the atomic Wehrl entropy. Moreover, we show that it is more convenient to use the Bloch sphere radius for quantifying entanglement in the JCM instead of these entropic relations.
The dynamical generation of entanglement in closed bipartite systems is investigated in the semiclassical regime. We consider a model of two particles, initially prepared in a product of coherent states, evolving in time according to a generic Hamiltonian, and derive a formula for the linear entropy of the reduced density matrix using the semiclassical propagator in the coherent-state representation. The formula is explicitly written in terms of quantities that define the stability of classical trajectories of the underlying classical system. The formalism is then applied to the problem of two nonlinearly coupled harmonic oscillators, and the result is shown to be in remarkable agreement with the exact quantum measure of entanglement in the short-time regime. An important by-product of our approach is a unified semiclassical formula, which contemplates both the coherent-state propagator and its complex conjugate.