Witnessing genuine multipartite entanglement with positive maps

Abstract

We derive a general framework that connects every positive map with a corresponding witness for partial separability in multipartite quantum systems. We show that many previous approaches were intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by non-decomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.

4 pages, 1 figure, this time the correct file and some last minute comments included

References in corpus (8)

• Entanglement detection
• 14-qubit entanglement: creation and coherence
• Taming multiparticle entanglement
• Optimal entanglement criterion for mixed quantum states
• Entanglement and permutational symmetry
• Determining lower bounds on a measure of multipartite entanglement from few local observables
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• A unified approach to entanglement criteria using the Cauchy-Schwarz and Hölder inequalities

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