Construction of multi-qubit optimal genuine entanglement witnesses

Abstract

We interpret multi-partite genuine entanglement witnesses as simultaneous positivity of various maps arising from them. We apply this result to multi-qubit {\sf X}-shaped Hermitian matrices, and characterize the conditions for them to be genuine entanglement witnesses, in terms of entries. Furthermore, we find all optimal ones among them. They turn out to have the spanning properties, and so they detect non-zero volume set of multi-qubit genuine entanglement. We also characterize decomposability for {\sf X}-shaped entanglement witnesses.

17 pages, to appear in Journal of Physics A: Mathematical and Theoretical

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• Nonexistence of $n$-qubit unextendible product bases of size $2^n-5$
• The role of phases in detecting three-qubit entanglement
• Separability of three qubit Greenberger-Horne-Zeilinger diagonal states
• Alternatives of entanglement depth and metrological entanglement criteria
• There exist infinitely many kinds of partial separability/entanglement
• Polytope structures for Greenberger-Horne-Zeilinger diagonal states
• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems