LPP elementary operator criterion of full separability for statesin multipartite quantum systems

YAN Si-Qing; HOU Jin-Chuan

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LPP elementary operator criterion of full separability for statesin multipartite quantum systems

YAN Si-Qing 1,HOU Jin-Chuan 2 *

1.Faculty of Mathematics, Taiyuan University of Technology, TaiYuan 030024

2.Faculty of Mathematics, Taiyuan University of Technology, TaYuan 030024

*Correspondence author

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Funding: This work is partially supported by National Natural ScienceFoundation of China （No.No. 11171249）, a grant fromInternational Cooperation Program in Sciences and Technology of Shanxi （No.2011081039）, Specialized Research Fund for the DoctoralProgram of Higher Education （No.20101402110012）

Opened online:26 September 2012

Accepted by: none

Citation: YAN Si-Qing,HOU Jin-Chuan.LPP elementary operator criterion of full separability for statesin multipartite quantum systems[OL]. [26 September 2012] http://en.paper.edu.cn/en_releasepaper/content/4490003

Let H1,H2,...,Hn,K (n≥2) be complex Hilbert spacesof finite or infinite dimension. A necessary and sufficientcriterion of full separability for multipartite states isestablished which says that a state ρ on H1×H2×...×Hn×K is fully separable if andonly if (∧×Id) ρ≥0 for all (finite rank)elementary operators ∧ from B(H1,H2,...,Hn) into B(K). Furthermore, acharacterization of LPP elementary operators and a method ofconstructing LPP elementary operators by positive elementary isgive. A new example is also presented to demonstrate how to applythe criterion to detect entanglement of tripartite states.

Keywords:Quantume information; multipartite quantum states; full separability; entanglement; elementary operators

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