Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps

2000/06/15 by Michał Horodecki, Michal Horodecki, Paweł Horodecki +2 · 3 citations
Computer Science · Physics and Astronomy · #Basis (linear algebra) #Bloch sphere #Linear map #Product (mathematics) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Qubit #quant-ph

paper · pdf · doi:10.1016/s0375-9601(01)00142-6

RevTeX, 7 pages

arxiv created 2000/06/15 · openalex publication_date 2001/05/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of n-1 particles. The method of providing of the maps on the basis of unextendable product bases is provided. The three qubit state problem is reformulated in the form suggesting possibility of explicite characterisation of all maps needed for separability condition.

Citations

• Bell inequalities and the separability criterion
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Multiparticle entanglement purification protocols
• Bound Entanglement Can Be Activated
• Separability Criterion for Density Matrices
• Multipartite pure-state entanglement
• Classification of multiqubit mixed states: Separability and distillability properties
• Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
• Optimization of entanglement witnesses
• Die gegenw�rtige Situation in der Quantenmechanik
• Separability of mixed states: necessary and sufficient conditions
• Quantifying Entanglement
• Quantum computing

Cited by

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• Displaced photon-number entanglement tests
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