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Keywords = Husimi distribution

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16 pages, 630 KiB  
Article
Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States
by Julio A. López-Saldívar, Olga V. Man’ko, Margarita A. Man’ko and Vladimir I. Man’ko
Entropy 2023, 25(12), 1628; https://doi.org/10.3390/e25121628 - 6 Dec 2023
Cited by 1 | Viewed by 2643
Abstract
The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator [...] Read more.
The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan–Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned. Full article
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17 pages, 332 KiB  
Article
Probability Distributions Describing Qubit-State Superpositions
by Margarita A. Man’ko and Vladimir I. Man’ko
Entropy 2023, 25(10), 1366; https://doi.org/10.3390/e25101366 - 22 Sep 2023
Cited by 3 | Viewed by 1781
Abstract
We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated [...] Read more.
We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
11 pages, 925 KiB  
Article
Quasi-Probability Husimi-Distribution Information and Squeezing in a Qubit System Interacting with a Two-Mode Parametric Amplifier Cavity
by Eied. M. Khalil, Abdel-Baset. A. Mohamed, Abdel-Shafy F. Obada and Hichem Eleuch
Mathematics 2020, 8(10), 1830; https://doi.org/10.3390/math8101830 - 19 Oct 2020
Cited by 8 | Viewed by 3290
Abstract
Squeezing and phase space coherence are investigated for a bimodal cavity accommodating a two-level atom. The two modes of the cavity are initially in the Barut–Girardello coherent states. This system is studied with the SU(1,1)-algebraic model. Quantum effects are analyzed with the Husimi [...] Read more.
Squeezing and phase space coherence are investigated for a bimodal cavity accommodating a two-level atom. The two modes of the cavity are initially in the Barut–Girardello coherent states. This system is studied with the SU(1,1)-algebraic model. Quantum effects are analyzed with the Husimi function under the effect of the intrinsic decoherence. Squeezing, quantum mixedness, and the phase information, which are affected by the system parameters, exalt a richer structure dynamic in the presence of the intrinsic decoherence. Full article
(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics)
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12 pages, 623 KiB  
Article
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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13 pages, 119 KiB  
Article
Fluctuations, Entropic Quantifiers and Classical-Quantum Transition
by Flavia Pennini and Angelo Plastino
Entropy 2014, 16(3), 1178-1190; https://doi.org/10.3390/e16031178 - 25 Feb 2014
Cited by 2 | Viewed by 5503
Abstract
We show that a special entropic quantifier, called the statistical complexity, becomes maximal at the transition between super-Poisson and sub-Poisson regimes. This acquires important connotations given the fact that these regimes are usually associated with, respectively, classical and quantum processes. Full article
(This article belongs to the Special Issue Maximum Entropy and Its Application)
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19 pages, 178 KiB  
Article
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 5729
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  
Review
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 9114
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  
Article
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  
Article
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
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