Sufficient and necessary condition of separability for generalized Werner states
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China)
In a celebrated paper [Optics Communications 179, 447, 2000], A.O. Pittenger and M.H. Rubin presented for the first time a sufficient and necessary condition of separability for the generalized Werner states. Inspired by their ideas, we generalized their method to a more general case. We obtain 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{sup [d{sup N}]}(v)=(1-v)(I{sup (N)})/(d{sup N}) +v|{psi}{sub d}{sup N}><{psi}{sub d}{sup N}|, where |{psi}{sub d}{sup N}>={sigma}{sub i=0}{sup d-1}{alpha}{sub i}|i...i> is an entangled pure state of N qudits system and {alpha}{sub i} satisfies two restrictions: (i) {sigma}{sub i=0}{sup d-1}{alpha}{sub i}{alpha}{sub i}*=1; (ii) Matrix 1/d (I{sup (1)}+T{sigma}{sub i{ne}}{sub j}{alpha}{sub i}|i><j|{alpha}{sub j}*), where T=Min{sub i{ne}}{sub j}{l_brace}1/|{alpha}{sub i}{alpha}{sub j}|{r_brace}, 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.
- OSTI ID:
- 21167716
- Journal Information:
- Annals of Physics (New York), Vol. 324, Issue 2; Other Information: DOI: 10.1016/j.aop.2008.12.006; PII: S0003-4916(08)00178-4; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
Similar Records
Criteria for exact qudit universality
Deterministic dense coding and entanglement entropy