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

Quantum entropy of radiation fields

Qiao Gu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Based on the elucidation for definition of entropy,we present a general method for calculating entropy of a quantum system in mixed state and apply it to the radiation fields in the typically mixed states.The results demonstrate that the quantum entropy is correlated to the microscopic fluctuation of the radiation fields,and it may therefore describe the quantum coherence properties of the radiation fields.As an example,the evolution of entropy of a dissipative quantum system is investigated then.The results obtained in this paper are expected to provide a basis for applications of entropy method in some fields,such as quantum optics,quantum informatics,biophotonics,and related interdisciplinary science.

Related papers

The maximum entropy principle for radiation fields

Qiao Gu

The maximum entropy principle discovered by Jaynes E T governs a search of the most reasonable probability assignment of stochastic variable,based on the measured data.One of the simplest applications of this principle lies in that all the thermodynamical relations are derived from the maximizing entropy of the system with energy as a single measured value.The maximum entropy principle is used then for the radiation field as a quantum system.Our results show that with an increase of the number of measurable quantities,the thermal field,the coherent states as well as the squeezed states are automatically introduced in turn;in particular,the dependence of all the properties of these radiation fields on the thermal noise is formulated quantitatively.The fundamental results obtained in this paper are expected to provide a basis for applications of the maximum entropy principle in some fields,such as quantum optics,quantum informatics,biophotonics,and related interdisciplinary science.

JOURNAL OF SHENZHEN UNIVERSITY SCIENCE AND ENGINEERING•Jan 1, 2011•1 citation

Quantum Features of Macroscopic Fields: Entropy and Dynamics

Robert Alicki

Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of the field combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equation for the reduced state of the field is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of entropy for the reduced state of the field follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows unifying the Mueller and Jones calculi in polarization optics.

arXiv:1904.06170•Entropy•Jul 18, 2019•9 citations

Invariant correlational entropy and complexity of quantum states

Valentin V. Sokolov, B. ALEX BROWN, Vladimir Zelevinsky

We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent Hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation independent, and can be calculated as a trace functional of the density matrix which describes the system in its interaction with the noise source. We analyze perturbation theory in order to show the evolution from the pure state to the mixed one. Exactly solvable examples illustrate the use of correlational entropy as a measure of the degree of complexity in comparison with other available suggestions such as basis-dependent information entropy. It is shown in particular that a harmonic oscillator in a uniform field of random strength comes to a quasithermal equilibrium; we discuss the relation between effective temperature and canonical equilibrium temperature. The notion of correlational entropy is applied to a realistic numerical calculation in the framework of the nuclear shell model. In this system, which reveals generic signatures of quantum chaos, correlational entropy and information entropy calculated in the mean field basis display similar qualitative behavior.

arXiv:chao-dyn/9709032•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 1, 1998•42 citations

Wehrl entropy and statistical properties of the radiation field in the excited and nonlinear binomial states

Ali Algarni, Abdullah M. Almarashi, S. Abdel Khalek

Objective: The study was conducted to estimate the nonlocal correlation between a single qubit and radiation field initially considered in the excited and nonlinear binomial distribution. Material and method: Explicit forms of the excited and nonlinear binomial states are presented. We investigate the dynamical properties of Wehrl entropy as an indicator of the statistical properties of the radiation field during the time evolution. The non-classicality of the field based on the evolution of Mandel parameter also discussed Results: Results of our study show that the Wehrl entropy, qubit-field entanglement and Mandel parameter at the periodic time are an opposite monotonic behavior. Also, a high amount of the entanglement is reached for a high value of deformation parameter. Finally the statistical properties of the field is Poissonian or sub-Poissonian photon distribution. Conclusion: It is concluded from the study that the Wehrl entropy and Mandel parameter were a good indications of the statistical and dynamical properties of the field during the interaction time.

Transylvanian Review•Jan 1, 2018•1 citation

Quantum statistics of nonclassical radiation in dissipative forward four-wave mixing. I. Method of generalized superposition of coherent and chaotic fields

Vlasta Peřinová, J. Křepelka

The Fokker-Planck equation approach to forward four-wave mixing developing from the initial coherent states is adopted to obtain a set of recursive relations for the expectation values of the normally ordered field operators. This set of equations is closed, in accordance with the model of the generalized superposition of coherent and chaotic fields, to provide differential equations for unknown quantities in this model. A numerical solution of these equations enables one to determine the photon number distribution, its factorial moments, squeezing variances, and entropy of radiation under discussion. Fully quantum-mechanical features of radiation such as its sub-Poisson behavior and squeezing of vacuum fluctuations are preserved in this approach. The validity of this approximation is discussed and numerical results are provided.

Physical Review A•Apr 1, 1989•2 citations

THE COHERENCE OF RADIATION AND INCREASE IN ENTROPY

Guang-jiong Ni, Suqing Chen, ZHOU GU-SHENG +1 more

A model of radiation by multi-atoms is discussed. System A, composed of N atoms with two energy levels, is coupled with a single-mode radiation B. A and B are in turn coupled with two thermal reservoirs D and C respectively, and we also assume that all atoms which are located within a wave length of the radiation field have the same phase. Then under the approximation of long wave, rotating wave and mean fields, by introducing Markov approximation after using the method of density matrix, we have derived the of equations motion for systems A and B respectively. These equations are concerning with the following processes: the spontaneous emission of single atom, the absorption and induced emission stimulated by thermal radiation, the induced emission of N atoms stimulated by single mode coherent state radiation as well as the coherent spontaneous emission of this multi-atoms system. The latter two processes are actually the two kinds of superradiance originated from Dicke model and had been investigated previonsly. We have analysed these five processes by numerical calculations. Besides, the influence of these processes upon the evolution of atomic system attaining thermal equilibrium and the increase of entropy is also discussed. It is pointed out that the correlations inside a multi-atoms system would not be destroyed by coherent spontaneous emission, in contrast with the incoherent one which leads to the change of entropy in atomic system. However, only when the entropy of the two reservoirs has been taken into account, will it be possible to demonstrate the mono-tonic increase in total entropy.

Acta Physica Sinica•Jan 1, 1982•0 citations
Based on the elucidation for definition of entropy,we present a general method for calculating entropy of a quantum system in mixed state and apply it to the radiation fields in the typically mixed states.The results demonstrate that the quantum entropy is correlated to the microscopic fluctuation of the radiation fields,and it may therefore describe the quantum coherence properties of the radiation fields.As an example,the evolution of entropy of a dissipative quantum system is investigated then.The results obtained in this paper are expected to provide a basis for applications of entropy method in some fields,such as quantum optics,quantum informatics,biophotonics,and related interdisciplinary science.
The maximum entropy principle discovered by Jaynes E T governs a search of the most reasonable probability assignment of stochastic variable,based on the measured data.One of the simplest applications of this principle lies in that all the thermodynamical relations are derived from the maximizing entropy of the system with energy as a single measured value.The maximum entropy principle is used then for the radiation field as a quantum system.Our results show that with an increase of the number of measurable quantities,the thermal field,the coherent states as well as the squeezed states are automatically introduced in turn;in particular,the dependence of all the properties of these radiation fields on the thermal noise is formulated quantitatively.The fundamental results obtained in this paper are expected to provide a basis for applications of the maximum entropy principle in some fields,such as quantum optics,quantum informatics,biophotonics,and related interdisciplinary science.
Macroscopic fields such as electromagnetic, magnetohydrodynamic, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of the field combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equation for the reduced state of the field is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of entropy for the reduced state of the field follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows unifying the Mueller and Jones calculi in polarization optics.
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent Hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation independent, and can be calculated as a trace functional of the density matrix which describes the system in its interaction with the noise source. We analyze perturbation theory in order to show the evolution from the pure state to the mixed one. Exactly solvable examples illustrate the use of correlational entropy as a measure of the degree of complexity in comparison with other available suggestions such as basis-dependent information entropy. It is shown in particular that a harmonic oscillator in a uniform field of random strength comes to a quasithermal equilibrium; we discuss the relation between effective temperature and canonical equilibrium temperature. The notion of correlational entropy is applied to a realistic numerical calculation in the framework of the nuclear shell model. In this system, which reveals generic signatures of quantum chaos, correlational entropy and information entropy calculated in the mean field basis display similar qualitative behavior.
Objective: The study was conducted to estimate the nonlocal correlation between a single qubit and radiation field initially considered in the excited and nonlinear binomial distribution. Material and method: Explicit forms of the excited and nonlinear binomial states are presented. We investigate the dynamical properties of Wehrl entropy as an indicator of the statistical properties of the radiation field during the time evolution. The non-classicality of the field based on the evolution of Mandel parameter also discussed Results: Results of our study show that the Wehrl entropy, qubit-field entanglement and Mandel parameter at the periodic time are an opposite monotonic behavior. Also, a high amount of the entanglement is reached for a high value of deformation parameter. Finally the statistical properties of the field is Poissonian or sub-Poissonian photon distribution. Conclusion: It is concluded from the study that the Wehrl entropy and Mandel parameter were a good indications of the statistical and dynamical properties of the field during the interaction time.
The Fokker-Planck equation approach to forward four-wave mixing developing from the initial coherent states is adopted to obtain a set of recursive relations for the expectation values of the normally ordered field operators. This set of equations is closed, in accordance with the model of the generalized superposition of coherent and chaotic fields, to provide differential equations for unknown quantities in this model. A numerical solution of these equations enables one to determine the photon number distribution, its factorial moments, squeezing variances, and entropy of radiation under discussion. Fully quantum-mechanical features of radiation such as its sub-Poisson behavior and squeezing of vacuum fluctuations are preserved in this approach. The validity of this approximation is discussed and numerical results are provided.
A model of radiation by multi-atoms is discussed. System A, composed of N atoms with two energy levels, is coupled with a single-mode radiation B. A and B are in turn coupled with two thermal reservoirs D and C respectively, and we also assume that all atoms which are located within a wave length of the radiation field have the same phase. Then under the approximation of long wave, rotating wave and mean fields, by introducing Markov approximation after using the method of density matrix, we have derived the of equations motion for systems A and B respectively. These equations are concerning with the following processes: the spontaneous emission of single atom, the absorption and induced emission stimulated by thermal radiation, the induced emission of N atoms stimulated by single mode coherent state radiation as well as the coherent spontaneous emission of this multi-atoms system. The latter two processes are actually the two kinds of superradiance originated from Dicke model and had been investigated previonsly. We have analysed these five processes by numerical calculations. Besides, the influence of these processes upon the evolution of atomic system attaining thermal equilibrium and the increase of entropy is also discussed. It is pointed out that the correlations inside a multi-atoms system would not be destroyed by coherent spontaneous emission, in contrast with the incoherent one which leads to the change of entropy in atomic system. However, only when the entropy of the two reservoirs has been taken into account, will it be possible to demonstrate the mono-tonic increase in total entropy.