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:0802.2169 · International Journal of Quantum Information

EVALUATING MEASURES OF NONCLASSICAL CORRELATION IN A MULTIPARTITE QUANTUM SYSTEM

AKIRA SAITOH, Robabeh Rahimi, Mikio Nakahara

Published Jul 1, 2008• 6 citations
arXivHTMLPDF

Abstract

We introduce and evaluate measures of nonclassical correlation defined on the basis of a paradigm claiming that a multipartite system represented by a density matrix having no product eigenbasis possesses nonclassical correlation.
DOI
10.1142/s0219749908004110

Related papers

Nonclassical correlation in a multipartite quantum system: Two measures and evaluation

Akira SaiToh, Robabeh Rahimi, Mikio Nakahara

There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic measures of nonclassical correlation of a multipartite quantum system. One is defined as the minimum uncertainty about a joint system after we collect outcomes of particular local measurements. The other is defined by taking the maximum over all local systems about the minimum distance between a genuine set and a mimic set of eigenvalues of a reduced density matrix of a local system. The latter measure is based on an artificial game to create mimic eigenvalues of a reduced density matrix of a local system from eigenvalues of a density matrix of a global system. Numerical computation of these measures for several examples is performed.

arXiv:quant-ph/0703133•Physical Review A•May 1, 2008•29 citations

Non-classical correlation in a multi-partite quantum system reconsidered

Akira Saitoh, Robabeh Rahimi, Mikio Nakahara

It is a popular idea that a multi-partite quantum system represented by a density matrix having no product eigenbasis possesses non-classical correlation. Supporting this idea, we define an entropic measure of non-classical correlation on the basis of the minimum uncertainty about a joint-system after we collect reports of particular local measurements. Numerical computation of this measure for several examples is performed.

•Mar 15, 2007•0 citations

ENTROPIC MEASURES OF NON-CLASSICAL CORRELATIONS

MATTHIAS D. LANG, Carlton M. Caves, Anil Shaji

A framework for categorizing entropic measures of non-classical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity obtained from measurements on the two systems. Three types of entropic quantities are used, and three different measurement strategies are applied to these quantities. Many of the resulting measures of non-classical correlations have been proposed previously. Properties of the various measures are explored, and results of evaluating the measures for two-qubit quantum states are presented.

arXiv:1105.4920•International Journal of Quantum Information•Oct 1, 2011•51 citations

NUMERICAL COMPUTATION OF TIME-DEPENDENT MULTIPARTITE NONCLASSICAL CORRELATION

AKIRA SAITOH, Robabeh Rahimi, Mikio Nakahara +1 more

•Apr 1, 2008•0 citations

Quantifying quantum coherence and nonclassical correlation based on Hellinger distance

Zhi‐Xiang Jin, Shao-Ming Fei

Quantum coherence and nonclassical correlation are key features of a quantum world. Quantifying coherence and nonclassical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum coherence by utilizing the Hellinger distance. This coherence measure is proven to fulfill all the criteria of a well-defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. In terms of this coherence measure, the distribution of quantum coherence in multipartite systems is studied and a corresponding polygamy relation is proposed. Its operational meanings and the relations between the generation of quantum correlations and the coherence are also investigated. Moreover, we present the Hellinger distance-based measure of nonclassical correlation, which not only inherits the nice properties of the Hellinger distance including contractivity, but also shows a powerful analytic computability for a large class of quantum states. We show that there is an explicit tradeoff relation satisfied by the quantum coherence and this nonclassical correlation.

arXiv:1806.10814•Physical Review A•Jun 27, 2018•60 citations

Single-experiment-detectable nonclassical correlation witness

Robabeh Rahimi, Akira SaiToh

Recent progress in theories of quantum information has determined nonclassical correlation defined differently from the widely used entanglement as an important property to evaluate computation and communication with mixed quantum states. We introduce an operational method to detect nonclassical correlation of bipartite systems. In this method, we use particular maps analogous to the well-established entanglement witnesses. Thus, the maps are called nonclassical correlation witness maps. Furthermore, it is proved that such a map can be generally decomposed so that a single-run experiment is feasible for implementation in bulk-ensemble systems.

arXiv:0911.3460•Physical Review A•Aug 11, 2010•38 citations
There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic measures of nonclassical correlation of a multipartite quantum system. One is defined as the minimum uncertainty about a joint system after we collect outcomes of particular local measurements. The other is defined by taking the maximum over all local systems about the minimum distance between a genuine set and a mimic set of eigenvalues of a reduced density matrix of a local system. The latter measure is based on an artificial game to create mimic eigenvalues of a reduced density matrix of a local system from eigenvalues of a density matrix of a global system. Numerical computation of these measures for several examples is performed.
A framework for categorizing entropic measures of non-classical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity obtained from measurements on the two systems. Three types of entropic quantities are used, and three different measurement strategies are applied to these quantities. Many of the resulting measures of non-classical correlations have been proposed previously. Properties of the various measures are explored, and results of evaluating the measures for two-qubit quantum states are presented.
Quantum coherence and nonclassical correlation are key features of a quantum world. Quantifying coherence and nonclassical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum coherence by utilizing the Hellinger distance. This coherence measure is proven to fulfill all the criteria of a well-defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. In terms of this coherence measure, the distribution of quantum coherence in multipartite systems is studied and a corresponding polygamy relation is proposed. Its operational meanings and the relations between the generation of quantum correlations and the coherence are also investigated. Moreover, we present the Hellinger distance-based measure of nonclassical correlation, which not only inherits the nice properties of the Hellinger distance including contractivity, but also shows a powerful analytic computability for a large class of quantum states. We show that there is an explicit tradeoff relation satisfied by the quantum coherence and this nonclassical correlation.
Recent progress in theories of quantum information has determined nonclassical correlation defined differently from the widely used entanglement as an important property to evaluate computation and communication with mixed quantum states. We introduce an operational method to detect nonclassical correlation of bipartite systems. In this method, we use particular maps analogous to the well-established entanglement witnesses. Thus, the maps are called nonclassical correlation witness maps. Furthermore, it is proved that such a map can be generally decomposed so that a single-run experiment is feasible for implementation in bulk-ensemble systems.