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20 pages, 1465 KiB

Open AccessArticle

A Numerical Study of Quantum Entropy and Information in the Wigner–Fokker–Planck Equation for Open Quantum Systems

by Arash Edrisi, Hamza Patwa and Jose A. Morales Escalante

Entropy 2024, 26(3), 263; https://doi.org/10.3390/e26030263 - 14 Mar 2024

Cited by 2 | Viewed by 2189

Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase [...] Read more.

Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase space description. We perform a numerical inspection of the Wehrl entropy for the benchmark problem of a harmonic potential, since the existence of a steady state and its analytical formula have been proven theoretically in this case. When there is friction in the noise terms, no theoretical results on the monotonicity of absolute entropy are available. We provide numerical results of the time evolution of the entropy in the case with friction using a stochastic (Euler–Maruyama-based Monte Carlo) numerical solver. For all the chosen initial conditions studied (all of them Gaussian states), up to the inherent numerical error of the method, one cannot disregard the possibility of monotonic behavior even in the case under study, where the noise includes friction terms. Full article

(This article belongs to the Special Issue 180th Anniversary of Ludwig Boltzmann)

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12 pages, 623 KiB

Open AccessArticle

Nonclassical Effects Based on Husimi Distributions in Two Open Cavities Linked by an Optical Waveguide

by Abdel-Baset A. Mohamed and Hichem Eleuch

Entropy 2020, 22(7), 767; https://doi.org/10.3390/e22070767 - 13 Jul 2020

Cited by 3 | Viewed by 2194

Abstract

Nonclassical effects are investigated in a system formed by two quantum wells, each of which is inside an open cavity. The cavities are spatially separated, linked by a fiber, and filled with a linear optical medium. Based on Husimi distributions (HDs) and Wehrl [...] Read more.

Nonclassical effects are investigated in a system formed by two quantum wells, each of which is inside an open cavity. The cavities are spatially separated, linked by a fiber, and filled with a linear optical medium. Based on Husimi distributions (HDs) and Wehrl entropy, we explore the effects of the physical parameters on the generation and the robustness of the mixedness and HD information in the phase space. The generated quantum coherence and the HD information depend crucially on the cavity-exciton and fiber cavity couplings as well as on the optical medium density. The HD information and purity are lost due to the dissipation. This loss may be inhibited by increasing the optical susceptibility as well as the couplings of the exciton-cavity and the fiber-cavity. These parameters control the regularity, amplitudes, and frequencies of the generated mixedness. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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12 pages, 2759 KiB

Open AccessArticle

Influence of the Coupling between Two Qubits in an Open Coherent Cavity: Nonclassical Information via Quasi-Probability Distributions

by Abdel-Baset A. Mohamed, Hichem Eleuch and Abdel-Shafy F. Obada

Entropy 2019, 21(12), 1137; https://doi.org/10.3390/e21121137 - 21 Nov 2019

Cited by 5 | Viewed by 2540

Abstract

In this paper, we investigate the dynamics of two coupled two-level systems (or qubits) that are resonantly interacting with a microwave cavity. We examine the effects of the intrinsic decoherence rate and the coupling between the two qubits on the non-classicality of different [...] Read more.

In this paper, we investigate the dynamics of two coupled two-level systems (or qubits) that are resonantly interacting with a microwave cavity. We examine the effects of the intrinsic decoherence rate and the coupling between the two qubits on the non-classicality of different system partitions via quasi-probability functions. New definitions for the partial Q-function and its Wehrl entropy are used to investigate the information and the quantum coherence of the phase space. The amount of the quantum coherence and non-classicality can be appropriately tuned by suitably adopting the rates of the intrinsic-decoherence and the coupling between the two qubits. The intrinsic decoherence has a pronounced effect on the negativity and the positivity of the Wigner function. The coupling between the two qubits can control the negativity and positivity of the quasi-probability functions. Full article

(This article belongs to the Collection Quantum Information)

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11 pages, 12848 KiB

Open AccessArticle

Quantum Interference Effects on Information Phase Space and Entropy Squeezing

by Abdel-Baset A. Mohamed, Shoukry S. Hassan and Rania A. Alharbey

Entropy 2019, 21(2), 147; https://doi.org/10.3390/e21020147 - 5 Feb 2019

Cited by 2 | Viewed by 2835

Abstract

Wehrl entropy and its density are used to investigate the dynamics of loss of coherence and information in a phase space for an atomic model of two-photon two-level atom coupled to different radiation reservoirs (namely, normal vacuum (NV), thermal field (TF) and squeezed [...] Read more.

Wehrl entropy and its density are used to investigate the dynamics of loss of coherence and information in a phase space for an atomic model of two-photon two-level atom coupled to different radiation reservoirs (namely, normal vacuum (NV), thermal field (TF) and squeezed vacuum (SV) reservoirs). Particularly, quantum interference (QI) effect, due to the 2-photon transition decay channels, has a paramount role in: (i) the atomic inversion decay in the NV case, which behaves as quantum Zeno and anti-Zeno decay effect; (ii) the coherence and information loss in the phase space; and (iii) identifying temporal information entropy squeezing. Results are also sensitive to the initial atomic state. Full article

(This article belongs to the Section Quantum Information)

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19 pages, 178 KiB

Open AccessArticle

Temperature Effects, Frieden–Hawkins’ Order-Measure, and Wehrl Entropy

by Flavia Pennini, Angelo Plastino and Gustavo L. Ferri

Entropy 2012, 14(11), 2081-2099; https://doi.org/10.3390/e14112081 - 26 Oct 2012

Cited by 5 | Viewed by 5727

Abstract

We revisit the Frieden–Hawkins’ Fisher order measure with a consideration of temperature effects. To this end, we appeal to the semiclassical approach. The order-measure’s appropriateness is validated in the semiclassical realm with regard to two physical systems. Insight is thereby gained with respect [...] Read more.

We revisit the Frieden–Hawkins’ Fisher order measure with a consideration of temperature effects. To this end, we appeal to the semiclassical approach. The order-measure’s appropriateness is validated in the semiclassical realm with regard to two physical systems. Insight is thereby gained with respect to the relationships amongst semiclassical quantifiers. In particular, it is seen that Wehrl’s entropy is as good a disorder indicator as the Frieden–Hawkins’ one. Full article

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21 pages, 266 KiB

Open AccessReview

Fisher Information and Semiclassical Treatments

by Flavia Pennini, Gustavo Ferri and Angelo Plastino

Entropy 2009, 11(4), 972-992; https://doi.org/10.3390/e11040972 - 3 Dec 2009

Cited by 13 | Viewed by 9108

Abstract

We review here the difference between quantum statistical treatments and semiclassical ones, using as the main concomitant tool a semiclassical, shift-invariant Fisher information measure built up with Husimi distributions. Its semiclassical character notwithstanding, this measure also contains abundant information of a purely quantal [...] Read more.

We review here the difference between quantum statistical treatments and semiclassical ones, using as the main concomitant tool a semiclassical, shift-invariant Fisher information measure built up with Husimi distributions. Its semiclassical character notwithstanding, this measure also contains abundant information of a purely quantal nature. Such a tool allows us to refine the celebrated Lieb bound for Wehrl entropies and to discover thermodynamic-like relations that involve the degree of delocalization. Fisher-related thermal uncertainty relations are developed and the degree of purity of canonical distributions, regarded as mixed states, is connected to this Fisher measure as well. Full article

(This article belongs to the Special Issue Maximum Entropy)

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10 pages, 221 KiB

Open AccessArticle

Information, Deformed қ-Wehrl Entropies and Semiclassical Delocalization

by Flavia Pennini, Angelo Plastino, Gustavo L. Ferri, Felipe Olivares and Montse Casas

Entropy 2009, 11(1), 32-41; https://doi.org/10.3390/e11010032 - 27 Jan 2009

Cited by 4 | Viewed by 7492

Abstract

Semiclassical delocalization in phase space constitutes a manifestation of the Uncertainty Principle, one indispensable part of the present understanding of Nature and the Wehrl entropy is widely regarded as the foremost localization-indicator. We readdress the matter here within the framework of the celebrated [...] Read more.

Semiclassical delocalization in phase space constitutes a manifestation of the Uncertainty Principle, one indispensable part of the present understanding of Nature and the Wehrl entropy is widely regarded as the foremost localization-indicator. We readdress the matter here within the framework of the celebrated semiclassical Husimi distributions and their associatedWehrl entropies, suitably қ-deformed. We are able to show that it is possible to significantly improve on the extant phase-space classical-localization power. Full article

(This article belongs to the Special Issue Information and Entropy)

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8 pages, 166 KiB

Open AccessArticle

Deformed Generalization of the Semiclassical Entropy

by Gustavo Ferri, Fernando Olivares, Flavia Pennini, Angel Plastino, Anel R. Plastino and Montserrat Casas

Entropy 2008, 10(3), 240-247; https://doi.org/10.3390/e10030240 - 19 Sep 2008

Cited by 1 | Viewed by 9861 | Correction

Abstract

We explicitly obtain here a novel expression for the semiclassical Wehrl’s entropy using deformed algebras built up with the q¡coherent states (see Arik and Coon [J.Math.Phys. 17, 524 (1976) and Quesne [J. Phys. A 35, 9213 (2002)]). The generalization is investigated with emphasis [...] Read more.

We explicitly obtain here a novel expression for the semiclassical Wehrl’s entropy using deformed algebras built up with the q¡coherent states (see Arik and Coon [J.Math.Phys. 17, 524 (1976) and Quesne [J. Phys. A 35, 9213 (2002)]). The generalization is investigated with emphasis on i) its behavior as a function of temperature and ii) the results obtained when the deformation-parameter tends to unity. Full article

(This article belongs to the Special Issue Facets of Entropy - Papers presented at the workshop in Copenhagen (24-26 October 2007))

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