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:1205.6016 · Journal of Physics A Mathematical and Theoretical

Detecting genuine multipartite correlations in terms of the rank of coefficient matrix

Bo Li, L. C. Kwek, Heng Fan

Published Nov 21, 2012• 9 citations
arXivHTMLPDF

Abstract

We propose a method to detect genuine quantum correlation for arbitrary quantum states in terms of the rank of coefficient matrices associated with the pure state. We then derive a necessary and sufficient condition for a quantum state to possess genuine correlation, namely that all corresponding coefficient matrices have rank larger than 1. We demonstrate an approach to decompose the genuine quantum correlated state with high rank coefficient matrix into the form of product states with no genuine quantum correlation for a pure state.

DOI
10.1088/1751-8113/45/50/505301

Related papers

Detection of genuine multipartite entanglement based on principal basis matrix representations

Hui Zhao, Yu-Qiu Liu, Shao-Ming Fei +2 more

Abstract We study the genuine multipartite entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect genuine multipartite entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.

arXiv:2202.06176•Laser Physics Letters•Feb 10, 2022•4 citations

Detection of genuine multipartite entanglement in arbitrary multipartite systems

Yu Shan Lu, Shao-Ming Fei

We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.

arXiv:2308.03245•Results in Physics•Aug 1, 2023•1 citation

Detecting genuine multipartite continuous-variable entanglement

Peter van Loock, Akira Furusawa

We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multiparty multimode continuous-variable state. Their violations can be sufficient for genuine multipartite entanglement, provided the combinations contain both conjugate variables of all modes. Hence, a complete state determination, for example, by detecting the entire correlation matrix of a Gaussian state, is not needed.

arXiv:quant-ph/0212052•Physical Review A•May 29, 2003•473 citations

Detecting genuine tripartite entanglement via general symmetric informationally complete measurements

Jia Hao, Hui Zhao, Shao-Ming Fei +2 more

We study multipartite entanglement and genuine tripartite entanglement based on general symmetric informationally complete positive operator valued measurements (GSIC-POVMs). By representing the bipartite density matrices in terms of GSIC-POVMs, we obtain the lower bound of the sum of squares of the corresponding probability. We then construct a special matrix with the correlation probability of GSIC-POVMs to derive useful and operational criteria to detect genuine tripartite entanglement. We also generalize the results to obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. Detailed examples show that the new method can detect more entangled and genuine entangled states than previous criteria.

Physical review. E•May 26, 2023•5 citations

Detecting genuine multipartite entanglement of pure states with bipartite correlations

Marcin Markiewicz, Wiesław Laskowski, Tomasz Paterek +1 more

Monogamy of bipartite correlations leads, for arbitrary pure multiqubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable of excluding the possibility of $k$ separability.

arXiv:1210.5530•Physical Review A•Mar 26, 2013•26 citations

Genuine correlated coherence

Tristan Kraft, Marco Piani

Abstract We introduce a notion of genuine correlated coherence. Such a notion is based on the possibility of concentrating on individual systems the coherence present in a distributed system, by making use of incoherent unitary transformations. We define an entropic quantifier of genuine correlated multipartite coherence for generic mixed states, and we focus on the bipartite pure-state case. In the latter case we derive necessary and sufficient conditions for the possibility of fully localizing the coherence, hence identifying the conditions for genuine correlated bipartite coherence. We analyze in detail the quantitative problem for the case of two-qubit pure states, identifying the states with the largest amount of genuine correlated coherence. Interestingly, such states do not have maximal global coherence nor maximal coherence rank.

arXiv:1801.03919•Journal of Physics A Mathematical and Theoretical•Mar 22, 2018•22 citations
We propose a method to detect genuine quantum correlation for arbitrary quantum states in terms of the rank of coefficient matrices associated with the pure state. We then derive a necessary and sufficient condition for a quantum state to possess genuine correlation, namely that all corresponding coefficient matrices have rank larger than 1. We demonstrate an approach to decompose the genuine quantum correlated state with high rank coefficient matrix into the form of product states with no genuine quantum correlation for a pure state.
Abstract We study the genuine multipartite entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect genuine multipartite entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.
We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.
We study multipartite entanglement and genuine tripartite entanglement based on general symmetric informationally complete positive operator valued measurements (GSIC-POVMs). By representing the bipartite density matrices in terms of GSIC-POVMs, we obtain the lower bound of the sum of squares of the corresponding probability. We then construct a special matrix with the correlation probability of GSIC-POVMs to derive useful and operational criteria to detect genuine tripartite entanglement. We also generalize the results to obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. Detailed examples show that the new method can detect more entangled and genuine entangled states than previous criteria.
Monogamy of bipartite correlations leads, for arbitrary pure multiqubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable of excluding the possibility of kkk separability.
Abstract We introduce a notion of genuine correlated coherence. Such a notion is based on the possibility of concentrating on individual systems the coherence present in a distributed system, by making use of incoherent unitary transformations. We define an entropic quantifier of genuine correlated multipartite coherence for generic mixed states, and we focus on the bipartite pure-state case. In the latter case we derive necessary and sufficient conditions for the possibility of fully localizing the coherence, hence identifying the conditions for genuine correlated bipartite coherence. We analyze in detail the quantitative problem for the case of two-qubit pure states, identifying the states with the largest amount of genuine correlated coherence. Interestingly, such states do not have maximal global coherence nor maximal coherence rank.