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The separability problem and normal completions
Journal article   Open access   Peer reviewed

The separability problem and normal completions

Hugo J. Woerdeman
Linear algebra and its applications, v 376(01-03), 85
2004
DOI: https://doi.org/10.1016/j.laa.2003.01.001
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https://doi.org/10.1016/j.laa.2003.01.001View
Published, Version of Record (VoR) Restricted

Abstract

Normal completions N× M separability
In this paper we introduce new normal completion problems that are directly related to the separability problem in quantum information. In fact we show that generically the N× M separability problem may be reduced in dimension via a multi-matrix normal completion problem. Specifying the result for the 2× M separability problem yields the equivalence to a normal completion problem that is a variation of the one introduced by P. Halmos. In addition, upper bounds on the number of states in a separable representation are given in terms of the normal completions.

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Mathematics
Mathematics, Applied
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