Separability of mixed states: necessary and sufficient conditions

1996/05/31 by Michał Horodecki, Michal Horodecki, Paweł Horodecki +2 · 113 citations
Computer Science · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Information and Cryptography #Spectral Theory in Mathematical Physics #quant-ph

paper · pdf · doi:10.1016/s0375-9601(96)00706-2

Revtex, 13 pages, replaced with minor typos corrected and some examples added

arxiv created 1996/06/26 · openalex publication_date 1996/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Separability Criterion for Density Matrices
• Die gegenw�rtige Situation in der Quantenmechanik
• Positive linear maps of operator algebras
• Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels

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