Detection of $k$-partite entanglement and $k$-nonseparability of multipartite quantum states

Abstract

Identifying the $k$-partite entanglement and $k$-nonseparability of general $N$-partite quantum states are fundamental issues in quantum information theory. By use of computable inequalities of nonlinear operators, we present some simple and powerful $k$-partite entanglement and $k$-nonseparability criteria that works very well and allow for a simple and inexpensive test for the whole hierarchy of $k$-partite entanglement and $k$-separability of $N$-partite systems with $k$ running from $N$ down to 2. We illustrate their strengths by considering several examples in which our criteria perform better than other known detection criteria. We are able to detect $k$-partite entanglement and $k$-nonseparabilty of multipartite systems which have previously not been identified. In addition, our results can be implemented in today's experiments.

10 pages

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• All multipartite entanglements are quantum coherences in locally distinguishable bases
• Detection of tripartite entanglement based on principal basis matrix representations
• Detecting multipartite entanglement via complete orthogonal basis
• Squashed Entanglement from Generalized Rindler Wedge
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• Optimal convex approximations of quantum states based on fidelity
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• Partitewise Entanglement
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