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:0904.4766 · International Journal of Quantum Information

A NOTE ON QUANTUM ENTANGLEMENT AND PPT

Shao-Ming Fei, Xianqing Li‐Jost

Published Apr 1, 2009• 5 citations
arXivHTMLPDF

Abstract

We study quantum states for which the PPT criterion is both sufficient and necessary for separability. We present a class of 3 × 3 bipartite mixed states and show that these states are separable if and only if they are PPT.
DOI
10.1142/s0219749909005328

Related papers

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

PPT classifiable families of bipartite states

Frank E. S. Steinhoff, M. C. de Oliveira

We construct a family of bipartite states of arbitrary dimension whose eigenvalues of the partially transposed matrix can be inferred directly from the block structure of the global density matrix. We identify from this several subfamilies in which the PPT criterion is both necessary and sufficient. A sufficient criterion of separability is obtained, which is fundamental for the discussion. We show how several examples of states known to be classifiable by the PPT criterion indeed belong to this general set. Possible uses of these states in numerical analysis of entanglement and in the search of PPT bound entangled states are briefly discussed.

Quantum Information and Computation•May 1, 2010•1 citation

Entangled States with Positive Partial Transpose in Any-Dimensional Quantum System

Yu-Chun Wu, Ping‐Xing Chen, Zheng-Wei Zhou +1 more

It is well known that the positive partial transpose (PPT) criterion for determining separability is an operational separability criterion. However, in a high-dimensional (>6) situation, this criterion is not sufficient. How can we judge whether an entangled state in any high-dimensional quantum system is PPT or not? Here we propose a linear algebra method for checking the positivity of the partial transpose of a state and present a set of entangled mixed states with non-positive partial transpose.

Chinese Physics Letters•Feb 24, 2005•2 citations

A sufficient and necessary criterion for separability of bipartite quantum states

Zhao, Hui Hui, Yu +1 more

中国物理B：英文版•Jan 1, 2014•0 citations

Separable Multipartite Mixed States: Operational Asymptotically Necessary and Sufficient Conditions

Fernando G. S. L. Brandão, Reinaldo O. Vianna

We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witnesses for every multipartite entangled state. This method provides an operational criterion for separability which is asymptotically necessary and sufficient. Our results are also generalized to detect all different types of multipartite entanglement.

arXiv:quant-ph/0405063•Physical Review Letters•Nov 24, 2004•71 citations

CRITERIA OF PARTIAL SEPARABILITY OF MULTIPARTITE QUBIT MIXED STATES

Zai-Zhe Zhong

We discuss the partial separability and its criteria problems of multipartite qubit mixed states. First, we strictly define what is the partial separability of a multipartite qubit system. Next, we provide a way of reduction from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that an N-partite qubit mixed state to be partially separable is its reduction to satisfy the PPT condition.

arXiv:quant-ph/0409182•International Journal of Quantum Information•May 31, 2005•2 citations
We construct a family of bipartite states of arbitrary dimension whose eigenvalues of the partially transposed matrix can be inferred directly from the block structure of the global density matrix. We identify from this several subfamilies in which the PPT criterion is both necessary and sufficient. A sufficient criterion of separability is obtained, which is fundamental for the discussion. We show how several examples of states known to be classifiable by the PPT criterion indeed belong to this general set. Possible uses of these states in numerical analysis of entanglement and in the search of PPT bound entangled states are briefly discussed.
It is well known that the positive partial transpose (PPT) criterion for determining separability is an operational separability criterion. However, in a high-dimensional (>6) situation, this criterion is not sufficient. How can we judge whether an entangled state in any high-dimensional quantum system is PPT or not? Here we propose a linear algebra method for checking the positivity of the partial transpose of a state and present a set of entangled mixed states with non-positive partial transpose.