Sufficient and Necessary Condition of Separability for Generalized Werner States

Details Sufficient and Necessary Condition of Separability for Generalized Werner States Sufficient and Necessary Condition of Separability for Generalized Werner States

2008-08-08

arxiv.org/abs/0808.1147v1

Annals of Physics 324, 408-413 (2009)

Physics

Quantum Physics

4 pages

Scientific paper

10.1016/j.aop.2008.12.006

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) $\sum_{i=0}^{d-1}\alpha_i\alpha_i^*=1$; (ii) Matrix $\frac{1}{d}(I^{(1)}+\mathcal{T}\sum_{i\neq j}\alpha_i|i>< j|\alpha_j^*)$, where $\mathcal{T}=\texttt{Min}_{i\neq j}\{1/|\alpha_i\alpha_j|\}$, 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.

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