Generalized reduction criterion for separability of quantum states

Abstract

A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new separability criterion naturally generalizes the reduction separability criterion introduced independently in previous work of [M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999)] and [N.J. Cerf, C. Adami and R.M. Gingrich, Phys. Rev. A 60, 898 (1999)]. In special cases, it recovers the previous reduction criterion and the recent generalized partial transposition criterion [K. Chen and L.A. Wu, Phys. Lett. A 306, 14 (2002)]. The criterion involves only simple matrix manipulations and can therefore be easily applied.

17 pages, 2 figures

References in corpus (6)

• Distinguishing separable and entangled states
• Separable states are more disordered globally than locally
• Some Properties of the Computable Cross Norm Criterion for Separability
• The generalized partial transposition criterion for separability of multipartite quantum states
• Separability of Rank Two Quantum States
• Necessary And Sufficient Condition of Separability of Any System

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