Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs

Abstract

We use Robust Semidefinite Programs and Entanglement Witnesses to study the distillability of Werner states. We perform exact numerical calculations which show 2-undistillability in a region of the state space which was previously conjectured to be undistillable. We also introduce bases which yield interesting expressions for the {\em distillability witnesses} and for a tensor product of Werner states with arbitrary number of copies.

arXiv comment16 pages, 2 figures

References in corpus (11)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Bound entanglement can be activated
• Evidence for Bound Entangled States with Negative Partial Transpose
• Distillability and partial transposition in bipartite systems
• Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
• Activating NPPT distillation with an infinitesimal amount of bound entanglement
• Witnessed Entanglement
• Characterization of Distillable and Activable States using Entanglement Witnesses

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