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:1504.02127 · Physica A Statistical Mechanics and its Applications

Quantum correlations from classically correlated states

Guido Bellomo, A. P. Majtey, Angel Ricardo Plastino, Angel Ricardo Plastino

Published Mar 17, 2014• 6 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2014.03.022

Related papers

Some New Properties of Quantum Correlations

Feng Liu, Fei Li, Yunxia Wei

International Journal of Theoretical Physics•Nov 19, 2016•0 citations

Characterization of quantum correlation in two-body quantum system by probability distribution

Guangrong Liu, Yang Liu, Xiangrong Li

The characterization of the correlation of quantum States plays a key role in the study of quantum information theory. Classical correlation is a quantum state that remains unchanged under local orthogonal projection, and it is not affected by decoherence. The entangled quantum state must be quantum correlation, and there is also quantum correlation in the separable quantum state. Relevance is a common phenomenon in nature. From the perspective of information theory, classical relevance can be described under Shannon's information theory. Therefore, it is necessary to explore the relationship among classical correlation, quantum correlation and quantum nonlocality. For the two-body quantum system, this paper gives the corresponding definitions of classical correlation state, left classical associated state and right classical associated state from the perspective of probability density, especially the definition of classical independent associated state. Different from the definition of local orthogonal projection measurement, it is easier to construct classical correlation state and quantum correlation state from the perspective of probability distribution, and further analyze the characteristics of eigenvalues and their corresponding eigenvectors. The selection of standard orthogonal basis, the corresponding relationship between separable ground state and classical correlation, entangled ground state and quantum correlation in two-body quantum system are studied. The corresponding characteristics of left classical correlation state and right classical correlation state are explored, and the relationship between separability and correlation, the relationship between convex combination and correlation of quantum States, and the left classical correlation state and right classical correlation state may also be quantum correlation States are illustrated by examples, and the definition of independent classical correlation state and its relationship with edge distribution are further obtained.

International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC)•Jul 21, 2024•0 citations

Robustness of quantum correlations against linear noise

Zhihua Guo, Huaixin Cao, Shixian Qu

Abstract Relative robustness of quantum correlations (RRoQC) of a bipartite state is firstly introduced relative to a classically correlated state. Robustness of quantum correlations (RoQC) of a bipartite state is then defined as the minimum of RRoQC of the state relative to all classically correlated ones. It is proved that as a function on quantum states, RoQC is nonnegative, lower semi-continuous and neither convex nor concave; especially, it is zero if and only if the state is classically correlated. Thus, RoQC not only quantifies the endurance of quantum correlations of a state against linear noise, but also can be used to distinguish between quantum and classically correlated states. Furthermore, the effects of local quantum channels on the robustness are explored and characterized.

Journal of Physics A Mathematical and Theoretical•Apr 4, 2016•3 citations

The limits of quantum correlations

Lê Phuc Thinh

Nature Physics•Mar 26, 2025•0 citations

Power of quantum channels for creating quantum correlations

Tahereh Abad, Vahid Karimipour, Laleh Memarzadeh

Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical channel [Phys. Rev. Lett. 107, 170502 (2011)]. We find the power of any given local channel for producing quantum correlations on an initially classically correlated state. We introduce a computable measure for quantifying the quantum correlations in quantum-classical states, which is based on the noncommutativity of ensemble states in one party of the composite system. Using this measure we show that the amount of quantum correlations produced is proportional to the classical correlations in the initial state. The power of an arbitrary channel for producing quantum correlations is found by averaging over all possible initial states. Finally, we compare our measure with the geometrical measure of quantumness for a subclass of quantum-classical sates, for which we have been able to find a closed analytical expression.

arXiv:1211.4805•Physical Review A•Dec 18, 2012•19 citations

Quantum and Classical Correlations in Quantum Measurement

Zhengjun Xi, Yongming Li

Foundations of Physics•Oct 11, 2012•6 citations
The characterization of the correlation of quantum States plays a key role in the study of quantum information theory. Classical correlation is a quantum state that remains unchanged under local orthogonal projection, and it is not affected by decoherence. The entangled quantum state must be quantum correlation, and there is also quantum correlation in the separable quantum state. Relevance is a common phenomenon in nature. From the perspective of information theory, classical relevance can be described under Shannon's information theory. Therefore, it is necessary to explore the relationship among classical correlation, quantum correlation and quantum nonlocality. For the two-body quantum system, this paper gives the corresponding definitions of classical correlation state, left classical associated state and right classical associated state from the perspective of probability density, especially the definition of classical independent associated state. Different from the definition of local orthogonal projection measurement, it is easier to construct classical correlation state and quantum correlation state from the perspective of probability distribution, and further analyze the characteristics of eigenvalues and their corresponding eigenvectors. The selection of standard orthogonal basis, the corresponding relationship between separable ground state and classical correlation, entangled ground state and quantum correlation in two-body quantum system are studied. The corresponding characteristics of left classical correlation state and right classical correlation state are explored, and the relationship between separability and correlation, the relationship between convex combination and correlation of quantum States, and the left classical correlation state and right classical correlation state may also be quantum correlation States are illustrated by examples, and the definition of independent classical correlation state and its relationship with edge distribution are further obtained.
Abstract Relative robustness of quantum correlations (RRoQC) of a bipartite state is firstly introduced relative to a classically correlated state. Robustness of quantum correlations (RoQC) of a bipartite state is then defined as the minimum of RRoQC of the state relative to all classically correlated ones. It is proved that as a function on quantum states, RoQC is nonnegative, lower semi-continuous and neither convex nor concave; especially, it is zero if and only if the state is classically correlated. Thus, RoQC not only quantifies the endurance of quantum correlations of a state against linear noise, but also can be used to distinguish between quantum and classically correlated states. Furthermore, the effects of local quantum channels on the robustness are explored and characterized.
Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical channel [Phys. Rev. Lett. 107, 170502 (2011)]. We find the power of any given local channel for producing quantum correlations on an initially classically correlated state. We introduce a computable measure for quantifying the quantum correlations in quantum-classical states, which is based on the noncommutativity of ensemble states in one party of the composite system. Using this measure we show that the amount of quantum correlations produced is proportional to the classical correlations in the initial state. The power of an arbitrary channel for producing quantum correlations is found by averaging over all possible initial states. Finally, we compare our measure with the geometrical measure of quantumness for a subclass of quantum-classical sates, for which we have been able to find a closed analytical expression.