Optimal indecomposable witnesses without extremality as well as spanning property
作者： Kil-Chan Ha , Hoseog Yu
DOI: 10.1088/1751-8113/45/39/395307
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摘要: One of the interesting problems on optimal indecomposable entanglement witnesses is whether there exists an witness which neither has spanning property nor associated with extremal positive linear map. Here, we answer this question negatively by examining extremality maps constructed Qi and Hou [J. Phys. A {\bf 44}, 215305 (2100)].
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Barbara M. Terhal, Bell inequalities and the separability criterion Physics Letters A. ,vol. 271, pp. 319- 326 ,(2000) , 10.1016/S0375-9601(00)00401-1
M. Lewenstein, B. Kraus, P. Horodecki, J. I. Cirac, Characterization of separable states and entanglement witnesses Physical Review A. ,vol. 63, pp. 044304- ,(2001) , 10.1103/PHYSREVA.63.044304
Man-Duen Choi, Positive semidefinite biquadratic forms Linear Algebra and its Applications. ,vol. 12, pp. 95- 100 ,(1975) , 10.1016/0024-3795(75)90058-0
G Sarbicki, Spectral properties of entanglement witnesses Journal of Physics A. ,vol. 41, pp. 375303- ,(2008) , 10.1088/1751-8113/41/37/375303
Xiaofei Qi, Jinchuan Hou, Characterization of optimal entanglement witnesses Physical Review A. ,vol. 85, pp. 022334- ,(2012) , 10.1103/PHYSREVA.85.022334
A. Jamiołkowski, An effective method of investigation of positive maps on the set of positive definite operators Reports on Mathematical Physics. ,vol. 5, pp. 415- 424 ,(1974) , 10.1016/0034-4877(74)90044-5
Hiroyuki Osaka, A Class of Extremal Positive Maps in 3×3 Matrix Algebras Publications of The Research Institute for Mathematical Sciences. ,vol. 28, pp. 747- 756 ,(1992) , 10.2977/PRIMS/1195167934
Remigiusz Augusiak, Gniewomir Sarbicki, Maciej Lewenstein, Optimal decomposable witnesses without the spanning property Physical Review A. ,vol. 84, pp. 052323- ,(2011) , 10.1103/PHYSREVA.84.052323
J. Sperling, W. Vogel, Necessary and sufficient conditions for bipartite entanglement Physical Review A. ,vol. 79, pp. 022318- ,(2009) , 10.1103/PHYSREVA.79.022318
Man-Duen Choi, Tsit-Yuen Lam, Extremal positive semidefinite forms Mathematische Annalen. ,vol. 231, pp. 1- 18 ,(1977) , 10.1007/BF01360024