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arXiv:2008.02730 · Quantum Information Processing

Necessary conditions for classifying $$\mathbf {m}$$-separability of multipartite entanglements

Wen Xu, Chuan-Jie Zhu, Zhu-Jun Zheng, Shao-Ming Fei

Published Jun 5, 2020• 6 citations
arXivHTMLPDF
DOI
10.1007/s11128-020-02705-6

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Necessary conditions for classifying m\mathbf {m}m-separability of multipartite entanglements
The reduction criterion is a well-known necessary condition for separable states, and states violating this condition are entangled and also 1-distillable. In this paper we introduce a set of necessary conditions for separability of multipartite states, obtained from a set of positive but not completely positive maps. These conditions can be thought of as generalizations of the reduction criterion to multipartite systems. We use tripartite Werner states as an example to investigate the entanglement detecting powers of some of these conditions, and we also look at what these conditions mean in terms of distillation. Finally, we show that these maps can be used to give a partial solution to the subsystem problem, as described by Butterley et al.