Sufficient and Necessary Condition of Separability for Generalized Werner States

Abstract

We introduce a sufficient and necessary condition for the separability of a specific class of $N$ $d$-dimensional system (qudits) states, namely special generalized Werner state (SGWS): $W^{[d^N]}(v)=(1-v)\frac{I^{(N)}}{d^N}+v|{\psi }_d^N><{\psi }_d^N|$, where $|{\psi }_d^N>={\sum }_{i=0}^{d-1}{\alpha }_i|i...i>$ is an entangled pure state of $N$ qudits system and ${\alpha }_i$ satisfys two restrictions: (i) ${\sum }_{i=0}^{d-1}{\alpha }_i{\alpha }_i^{\ast }=1$; (ii) Matrix $\frac{1}{d}(I^{(1)}+\mathcal{T}{\sum }_{i\ne j}{\alpha }_i|i><j|{\alpha }_j^{\ast })$, where $\mathcal{T}={\text{Min}}_{i\ne j}\{1/|{\alpha }_i{\alpha }_j|\}$, is a density matrix. Our condition gives quite a simple and efficiently computable way to judge whether a given SGWS is separable or not and previously known separable conditions are shown to be special cases of our approach.

4 pages

References in corpus (1)

• Experimental quantum teleportation

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