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

Infinite Dimensional Analysis Quantum Probability and Related Topics

Horodeckis criterion of separability of mixed states in von Neumann and C*-algebras

Marek Miller, Robert Olkiewicz

Published Nov 13, 2014• 4 citations
Publisher

Abstract

The Horodeckis necessary and sufficient condition of separability of mixed states is generalized to arbitrary composite quantum systems.
DOI
10.1142/s0219025714500283

Related papers

A Separability of mixed states: necessary and sufficient conditions

Michał Horodecki, Paweł Horodecki, Ryszard Horodecki

We provide necessary and sufficient conditions for the separability of mixed states. As a result we obtain a simple criterion of the separability for 2 x 2 and 2 x 3 systems. Here, the positivity of the partial transposition of a state is necessary and sufficient for its separability. However, this is not the case in general. Some examples of mixtures which demonstrate the utility of the criterion are considered.

•Jan 1, 1996•2,276 citations

Comment on: Necessary and sufficient condition of separability of any system

Tilo Eggeling, K. G. H. Vollbrecht, Michael M. Wolf

In a recent paper (quant-ph/0102133) Chen, Liang, Li and Huang suggest a necessary and sufficient separability criterion, which is supposedly practical in judging the separability of any mixed state. In this note we briefly recapitulate their main result and show that it is a reformulation of the problem rather than a practical criterion.

arXiv:quant-ph/0103003•Mar 1, 2001•1 citation

A sufficient and necessary criterion for separability of bipartite quantum states

Hui Zhao, Xinyu Yu

A sufficient and necessary criterion for separability of bipartite quantum states is presented. We construct a class of mixed states in 2 ⊗ k quantum systems and in 3 ⊗ k quantum systems, respectively and show that these states are separable if and only if they are positive partial transpositions.

Chinese Physics B•Jul 31, 2014•0 citations

Necessary and sufficient condition of separability of any system

Ping‐Xing Chen, Lin-Mei Liang, Cheng-Zu Li +1 more

The necessary and sufficient condition of the separability of a mixed state of any system is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled decomposition of a separable mixed state.

arXiv:quant-ph/0102133•Physical Review A•Apr 16, 2001•10 citations

A Necessary and Sufficient Criterion for the Separability of Quantum State

Junli Li, Cong‐Feng Qiao

Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn's problem. The work follows the work initiated by Horodecki et al. and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state.

arXiv:1607.03364•Scientific Reports•Jan 17, 2018•33 citations

A separability criterion for density operators

Oliver Rudolph

We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.

arXiv:quant-ph/0002026•Journal of Physics A Mathematical and General•May 18, 2000•75 citations
Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn's problem. The work follows the work initiated by Horodecki et al. and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state.