Reflections upon separability and distillability

2001/10/12 by Dagmar Bruß, D. Bruss, J. I. Cirac +9 · 11 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1080/09500340110105975

published as J. Mod. Opt. 49, 1399-1418 (2002) · 12 pages, 7 figures, proceedings of the ESF QIT Conference Gdansk, July 2001, submitted to special issue of J. Mod. Opt

arxiv created 2001/10/12 · openalex publication_date 2002/07/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

We present an abstract formulation of the so-called Innsbruck-Hannover programme that investigates quantum correlations and entanglement in terms of convex sets. We present a unified description of optimal decompositions of quantum states and the optimization of witness operators that detect whether a given state belongs to a given convex set. We illustrate the abstract formulation with several examples, and discuss relations between optimal entanglement witnesses and n-copy non-distillable states with non-positive partial transpose.

Citations

• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Separability Criterion for Density Matrices
• Die gegenw�rtige Situation in der Quantenmechanik
• Positive linear maps of operator algebras

Cited by

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• Local observables for entanglement detection of depolarized states
• Lower bounds of concurrence for tripartite quantum systems
• Mapping the spatial distribution of entanglement in optical lattices
• Unifying several separability conditions using the covariance matrix criterion
• Reliable entanglement verification
• John Bell and the nature of the quantum world
• Characterizing Entanglement via Uncertainty Relations
• Entropic uncertainty relations and entanglement