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Chinese Physics Letters

Separability Criteria for Quantum Mixed States in Terms of Trace Norm

Hui Zhao

Published Jun 28, 2006• 3 citations
Publisher

Abstract

A new necessary conditions for separability of mixed states in bipartite and multipartite quantum systems of arbitrary dimensions are presented. This method requires only a few local measurements. If a quantum state in a bipartite (or multipartite) system of arbitrary dimension is separable, we show that the trace norm of a constructive matrix is less than or equal to 1.

DOI
10.1088/0256-307x/23/7/005

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A new necessary conditions for separability of mixed states in bipartite and multipartite quantum systems of arbitrary dimensions are presented. This method requires only a few local measurements. If a quantum state in a bipartite (or multipartite) system of arbitrary dimension is separable, we show that the trace norm of a constructive matrix is less than or equal to 1.
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The purpose of this paper is to obtain a sufficient and necessary condition as a criteria to test whether an arbitrary multipartite state is entangled or not. Based on the tensor expression of a multipartite pure state, the paper shows that a state is separable iff $| \mathbf{C}(ρ)| $ =0 for pure states and iff C(ρ)C(ρ)C(ρ) vanishes for mixed states.