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:2609.34859 · Journal of Statistical Physics

Correlation measure for statistical systems

V. I. Yukalov, E. P. Yukalova

quant-phcond-mat.stat-mechSubmitted Sep 28, 2026• Announced Sep 29, 2026• 1 citation
arXivHTMLPDF

Abstract

A measure of correlations for statistical systems is advanced, called correlation index. The measure is general, being applicable to quantum and classical, equilibrium and nonequilibrium statistical systems. After formulating the general notion of correlation indices for arbitrary trace-class operators, the calculation of the correlation indices are illustrated by several examples of density operators and reduced density matrices. The computation of the correlation indices for equilibrium systems is exemplified for bosonic systems with the Bose-Einstein condensate, superconducting systems, and for spin systems. Correlation indices for nonequilibrium systems are considered for nonlinear dynamics of spin and pseudospin systems.

Journal reference
J. Stat. Phys. 193 (2026) 112
Comments
23 pages, 4 figures

Related papers

Measuring correlations in quantum and statistical systems

V. I. Yukalov, E. P. Yukalova

The survey discusses the problem of measuring correlations in composite quantum and statistical systems. After briefly recalling the standard methods of describing correlations, the emphasis is on the method of correlation indices. The latter method for quantifying the strength of correlations in composite physical systems is sufficiently general allowing for measuring in a unique way the correlation strength in both quantum and statistical systems, for static as well as for dynamic processes. The correlation indices, can be defined for correlation operators, reduced density matrices, and other operators containing information on correlations in the studied composite systems. The correlation indices measure all types of correlations, quantum correlations, such as entanglement, as well as classical correlations. They are applicable for characterizing static as well as dynamical processes. Examples are given of correlation indices for several quantum states and for spin and pseudospin systems. The quantification of correlations in a nonequilibrium system is exemplified by calculating the correlation index for a trapped Bose-Einstein condensate subject to the action of an alternating field.

quant-pharXiv:2609.18412•Laser Physics Letters•Sep 17, 2026•0 citations

EVOLUTIONAL ENTANGLEMENT IN NONEQUILIBRIUM PROCESSES

Vyacheslav I. Yukalov

Entanglement in nonequilibrium systems is considered. A general definition for entanglement measure is introduced, which can be applied for characterizing the level of entanglement produced by arbitrary operators. Applying this definition to reduced density matrices makes it possible to measure the entanglement in nonequilibrium as well as in equilibrium statistical systems. An example of a multimode Bose–Einstein condensate is discussed.

arXiv:quant-ph/0309037•Modern Physics Letters B•Feb 10, 2003•24 citations

Quantifying entanglement production of quantum operations

Vyacheslav I. Yukalov

The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic. A particular case is the entanglement produced by a density operator or a density matrix. The suggested measure is valid for operations over pure states as well as over mixed states, for equilibrium as well as nonequilibrium processes. Systems of arbitrary nature can be treated, described by field operators, spin operators, or any other kind of operator that is realized by constructing generalized density matrices. The interplay between entanglement production and phase transitions in statistical systems is analyzed using the examples of Bose-Einstein condensation, the superconducting transition, and magnetic transitions. The relation between the measure of entanglement production and order indices is analyzed.

arXiv:quant-ph/0309054•Physical Review A•Aug 25, 2003•35 citations

Entanglement Measure for Composite Systems

Vyacheslav I. Yukalov

A general description of entanglement is suggested as an action realized by an arbitrary operator over given disentangled states. The related entanglement measure is defined. Because of its generality, this definition can be employed for any physical systems, pure or mixed, equilibrium or nonequilibrium, and characterized by any type of operators, whether these are statistical operators, field operators, spin operators, or anything else. Entanglement of any number of parts from their total ensemble forming a multiparticle composite system can be determined. Interplay between entanglement and ordering, occurring under phase transitions, is analyzed by invoking the concept of operator order indices.

arXiv:quant-ph/0309015•Physical Review Letters•Apr 24, 2003•38 citations

Complexity of finite statistical systems

Vyacheslav I. Yukalov, Elizaveta P. Yukalova

Abstract The paper advances a novel notion–Complexity of Statistical Systems which is applicable to both, infinite systems in the thermodynamic limit as well as to finite systems, such as the systems of trapped atoms and molecules. The notion takes into account the level of ordering and the strength of correlations in the system. Illustrations are given by presenting calculations of complexity for finite systems with Bose–Einstein condensate and for superfluid systems.

Laser Physics Letters•Oct 1, 2026•0 citations

Measure of Entanglement Production by Quantum Operations

Vyacheslav I. Yukalov, Elizaveta P. Yukalova

Abstract A measure of entanglement production by quantum operations is suggested. This measure is general, being valid for operations over pure states as well as over mixed states, for equilibrium as well as for nonequilibrium processes. The measure of entanglement production satisfies all properties typical of such a characteristic. Systems of arbitrary nature can be treated, described by field operators, spin operators, or any other operators, which is realized by defining generalized correlation matrices. Particular cases of entanglement production are considered.

arXiv:2507.23366•Physics of Particles and Nuclei•Aug 1, 2025•1 citation
A measure of correlations for statistical systems is advanced, called correlation index. The measure is general, being applicable to quantum and classical, equilibrium and nonequilibrium statistical systems. After formulating the general notion of correlation indices for arbitrary trace-class operators, the calculation of the correlation indices are illustrated by several examples of density operators and reduced density matrices. The computation of the correlation indices for equilibrium systems is exemplified for bosonic systems with the Bose-Einstein condensate, superconducting systems, and for spin systems. Correlation indices for nonequilibrium systems are considered for nonlinear dynamics of spin and pseudospin systems.
The survey discusses the problem of measuring correlations in composite quantum and statistical systems. After briefly recalling the standard methods of describing correlations, the emphasis is on the method of correlation indices. The latter method for quantifying the strength of correlations in composite physical systems is sufficiently general allowing for measuring in a unique way the correlation strength in both quantum and statistical systems, for static as well as for dynamic processes. The correlation indices, can be defined for correlation operators, reduced density matrices, and other operators containing information on correlations in the studied composite systems. The correlation indices measure all types of correlations, quantum correlations, such as entanglement, as well as classical correlations. They are applicable for characterizing static as well as dynamical processes. Examples are given of correlation indices for several quantum states and for spin and pseudospin systems. The quantification of correlations in a nonequilibrium system is exemplified by calculating the correlation index for a trapped Bose-Einstein condensate subject to the action of an alternating field.
The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic. A particular case is the entanglement produced by a density operator or a density matrix. The suggested measure is valid for operations over pure states as well as over mixed states, for equilibrium as well as nonequilibrium processes. Systems of arbitrary nature can be treated, described by field operators, spin operators, or any other kind of operator that is realized by constructing generalized density matrices. The interplay between entanglement production and phase transitions in statistical systems is analyzed using the examples of Bose-Einstein condensation, the superconducting transition, and magnetic transitions. The relation between the measure of entanglement production and order indices is analyzed.
A general description of entanglement is suggested as an action realized by an arbitrary operator over given disentangled states. The related entanglement measure is defined. Because of its generality, this definition can be employed for any physical systems, pure or mixed, equilibrium or nonequilibrium, and characterized by any type of operators, whether these are statistical operators, field operators, spin operators, or anything else. Entanglement of any number of parts from their total ensemble forming a multiparticle composite system can be determined. Interplay between entanglement and ordering, occurring under phase transitions, is analyzed by invoking the concept of operator order indices.
Abstract A measure of entanglement production by quantum operations is suggested. This measure is general, being valid for operations over pure states as well as over mixed states, for equilibrium as well as for nonequilibrium processes. The measure of entanglement production satisfies all properties typical of such a characteristic. Systems of arbitrary nature can be treated, described by field operators, spin operators, or any other operators, which is realized by defining generalized correlation matrices. Particular cases of entanglement production are considered.