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/0207130

Algebraic-geometric separability criterion and low rank mixed state entanglement

Chen, Hao

Published Jul 22, 2002• 0 citations
arXivHTMLPDF

Abstract

We first propose a new separability criterion based on algebraic-geometric invariants of bipartite mixed states introduced in [1], then prove that for all low ranks r
DOI
10.48550/arxiv.quant-ph/0207130

Related papers

Random low rank mixed states are entangled

H Chen

We prove that random rank r<2m-2 mixed states in bipartite mxm systems are entangled based on algebraic-geometric separability criterion proved in [1]. This also means that the algebraic-geometric separability criterion can be used to detect all low rank entangled mixed states outside a measure zero set.

•Nov 1, 2001•0 citations

New Invariants and Separability criterion of the Mixed States: Bipartite Case

Hao Chen

We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear subspaces if the mixed state is separable. Some examples are given and studied based on our criterion

arXiv:quant-ph/0107111•Jul 23, 2001•1 citation

Random low rank mixed states are highly entangled

Chen, Hao

We prove that for many ranks r<2m-2, random rank r mixed states in bipartite mxm systems have relatively high Schmidt numbers, which is based on algebraic-geometric separability criterion proved in [1]. This also means that the algebraic-geometric separability criterion can be used to detect all low rank entangled mixed states outside a measure zero set.

arXiv:quant-ph/0111004•Nov 1, 2001•0 citations

New Invariants and Separability Criterion of the Mixed States: Multipartite Case

Chen, Hao

We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear subspaces if the state is separable. Some examples are studied based on our criterion

arXiv:quant-ph/0107112•Jul 23, 2001•0 citations

Schmidt number of pure states in bipartite quantum systems as an algebraic-geometric invariant

Hao Chen

Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept, is actually an algebraic-geometric invariant.

arXiv:quant-ph/0108034•Aug 8, 2001•0 citations

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