General scheme for construction of scalar separability criteria from positive maps

2007/09/30 by Remigiusz Augusiak, Julia Stasińska
Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #Matrix Theory and Algorithms #Quantum Information and Cryptography #quant-ph

paper · pdf · doi:10.1103/physreva.77.010303

published as Physical Review A 77, 010303(R) (2008) · RevTex, 5 pages, 2 figures, the revised version

openalex publication_date 2008/01/28 · arxiv created 2008/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a general scheme allowing for construction of scalar separability criteria from positive, but not completely positive, maps. The concept is based on a decomposition of every positive map \ensuremathΛ acting on M_d(ℂ) into a difference of two completely positive maps \ensuremathΛ₁, \ensuremathΛ₂, i.e., \ensuremathΛ=\ensuremathΛ₁\ensuremath-\ensuremathΛ₂. The scheme may also be treated as a generalization of the known entropic inequalities, which are obtained from the reduction map. Analyses performed on a few classes of states show that the scalar criteria are stronger than the entropic inequalities and when derived from indecomposable maps allow for detection of bound entanglement.

Citations

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