Y. Z. WANG, D. X. WANG

Copyright © 2012 SciRes. JQIS

81

According by Theorem 2.1, by a straightforward cal-

culation, we obtain the following result, if

1

05

x,

then

2222

00

xyz

TrMMMM (20)

so

is entangled.

Remark: It is obvious that this criterion of Theorem

2.1 is weaker than PPT criterion [4], in fact if x ≠ 1,

is also entangled, but this criterion give us a method to

detect the entanglement for states in infinite bipartite

quantum systems.

4. Acknowledgements

This work was partially supported by the National Natu-

ral Science Foundation of China (11171249) and the

Natural Science Foundation of Shanxi Province

(2011021002-2). The authors also wish to give their

thanks to the referees for their comments to improve the

presentation of this paper.

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