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:quant-ph/0107147 · Journal of Modern Optics

Concurrence in arbitrary dimensions

Piotr Badziag, Piotr Deuar, Michał Horodecki, Paweł Horodecki, Ryszard Horodecki

Published Jul 1, 2002• 51 citations
arXivHTMLPDF

Abstract

We argue that a complete characterization of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multidimensional generalizations of concurrence and find evidence that they may provide useful tools for the analysis of quantum correlations in mixed bipartite states. We also introduce biconcurrence that leads to a necessary and sufficient condition for separability.

DOI
10.1080/09500340210121589

Related papers

Concurrence in arbitrary dimensions

Piotr Badziąg, Piotr Deuar, Michał Horodecki +2 more

We argue that a complete characterisation of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multi-dimensional generalizations of concurrence and find evidence that they may provide useful tools for the analysis of quantum correlations in mixed bipartite states. We also introudce {\\it biconcurrence} that leads to a necessary and sufficient condition for separability.

•Jul 30, 2001•60 citations

A note on generalized concurrences and entanglement detection

Cattaneo, Laura, Domenico D’Alessandro

We study generalized concurrences as a tool to detect the entanglement of bipartite quantum systems. By considering the case of 2 X 4 states of rank 2, we prove that generalized concurrences do not, in general, give a necessary and sufficient condition of separability. We identify a set of entangled states which are undetected by this method.

arXiv:0804.3620•Apr 22, 2008•1 citation

Generalized concurrences do not provide necessary and sufficient conditions for entanglement detection

L. Cattaneo, Domenico D’Alessandro

We study generalized concurrences as a tool to detect the entanglement of bipartite quantum systems. By considering the case of 2x4 states of rank 2, we prove that generalized concurrences do not, in general, give a necessary and sufficient condition of separability. We identify a set of entangled states which are undetected by this method.

Quantum Information and Computation•Jan 1, 2009•0 citations

Necessary and sufficient range-dimension conditions for bipartite quantum correlations

Fedor Herbut

As is well known, every mixed or pure state of a bipartite quantum system is given by a statistical operator, which determines, in terms of its two reduced statistical operators, the subsystem states. Necessary and sufficient conditions for the existence of a composite-system state, and, separately, for the possibility of its being correlated or uncorrelated in terms of the range dimensions of the three mentioned statistical operators are derived. As a corollary, it is shown that it cannot happen that two of the mentioned dimensions are finite and the third is infinite.

arXiv:quant-ph/0305173•Journal of Physics A Mathematical and General•Aug 20, 2002•0 citations

Concurrence of Mixed Bipartite Quantum States in Arbitrary Dimensions

Florian Mintert, Marek Kuś, Andreas Buchleitner

We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with a positive partial transpose.

arXiv:quant-ph/0403063•Physical Review Letters•Apr 23, 2004•252 citations

Separability Criteria for Quantum Mixed States in Terms of Trace Norm

Hui Zhao

A new necessary conditions for separability of mixed states in bipartite and multipartite quantum systems of arbitrary dimensions are presented. This method requires only a few local measurements. If a quantum state in a bipartite (or multipartite) system of arbitrary dimension is separable, we show that the trace norm of a constructive matrix is less than or equal to 1.

Chinese Physics Letters•Jun 28, 2006•3 citations
We argue that a complete characterization of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multidimensional generalizations of concurrence and find evidence that they may provide useful tools for the analysis of quantum correlations in mixed bipartite states. We also introduce biconcurrence that leads to a necessary and sufficient condition for separability.
As is well known, every mixed or pure state of a bipartite quantum system is given by a statistical operator, which determines, in terms of its two reduced statistical operators, the subsystem states. Necessary and sufficient conditions for the existence of a composite-system state, and, separately, for the possibility of its being correlated or uncorrelated in terms of the range dimensions of the three mentioned statistical operators are derived. As a corollary, it is shown that it cannot happen that two of the mentioned dimensions are finite and the third is infinite.