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A matrix realignment method for recognizing entanglement

Kai Chen·Ling-An Wu
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Abstract

Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any separable state, the sum of the singular values of the matrix should be less than or equal to 1. This condition provides a very simple, computable necessary criterion for separability, and shows powerful ability to identify most bound entangled states discussed in the literature. As a byproduct of the criterion, we give an estimate for the degree of entanglement of the quantum state.

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Kai Chen, Ling-An Wu. 2003-04-28. A matrix realignment method for recognizing entanglement. https://arxiv.org/abs/quant-ph/0205017

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