参考文献:1. Brandao, F.G.S.L., Vianna, R.O.: Witnessed entanglement. Int. J. Quantum Inf. 4, 331鈥?40 (2006) CrossRef 2. Dong, D.Y., Lam, J., Tarn, T.J.: Rapid incoherent control of quantum systems based on continuous measurements and reference model. IET Control Theory Appl. 3, 161鈥?69 (2009) CrossRef 3. Martina, L., Ruggeri, G., Soliani, G.: Correlation energy and entanglement gap in continuous models. Int. J. Quantum Inf. 9, 843鈥?62 (2011) CrossRef 4. Terhal, B.M.: Detecting quantum entanglement. Theor. Comput. Sci. 287, 313鈥?35 (2002) CrossRef 5. Younes, A., Rowe, J., Miller, J.: Enhanced quantum searching via entanglement and partial diffusion. Phys. D 237, 1074鈥?078 (2008) CrossRef 6. Zhao, S.W., Lin, H., Sun, J.T., Xue, Z.G.: An implicit Lyapunov control for finite-dimensional closed quantum systems. Int. J. Robust Nonlinear Control 22, 1212C1228 (2011) 7. Choi, M.D.: Positive semidefinite biquadratic forms. Linear Algebra Appl. 12, 95鈥?00 (1975) 8. Eom, M.H., Kye, S.H.: Duality for positive linear maps in matrix algebras. Math. Scand 86, 130鈥?42 (2000) 9. Yosida, K.: Functional Analysis. Springer, Berlin (1999) 10. Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1鈥? (1996) CrossRef 11. Horodecki, M., Horodecki, P., Horodecki, R.: Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps. Phys. Lett. A 283, 1鈥? (2001) CrossRef 12. Lewenstein, M., Kraus, B., Cirac, J.I., Horodecki, P.: Optimization of entanglement witness. Phys. Rev. A 62, 052310 (2000) CrossRef 13. Terhal, B.M.: Bell inequalities and the separability criterion. Phys. Lett. A 271, 319鈥?26 (2000) CrossRef 14. Maziero, J., Serra, R.M.: Classicality witness for two-qubit states. Int. J. Quantum Inf. 10, 1250028 (2012) CrossRef 15. G眉hne, O., T贸th, G.: Entanglement detection. Phys. Rep. 474, 1鈥?5 (2009) CrossRef 16. Wu, Y.C., Guo, G.C.: Determining the existence of the common entanglement witnesses for some entangled states. Phys. Rev. A 75, 052333 (2007) CrossRef 17. Chru艣ci艅ski, D., Sarbicki, G.: Entanglement witness: construction, analysis and classification. arXiv:1402.2413 18. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865鈥?42 (2009) CrossRef 19. Gorini, V., Sudarshan, E.C.G.: Extreme affine transformations. Commun. Math. Phys. 46, 43鈥?2 (1976) CrossRef 20. Ha, K.C., Kye, S.H.: Entanglement witnesses arising from exposed positive linear maps. Open Syst. Inf. Dyn. 18, 323鈥?37 (2011) CrossRef 21. Jamiolkowski, A.: Linear transformations which preserve trace and positive semi-definiteness of operators. Rep. Math. Phys. 3, 5275 (1972) CrossRef 22. Skowronek, L.: Dualities and positivity in the study of quantum entanglement. Int. J. Quantum Inf. 8, 721鈥?54 (2011) CrossRef 23. Chru艣ci艅ski, D., Kossakowski, A.: Geometry of quantum states: new construction of positive maps. Phys. Lett. A 373, 2301鈥?305 (2009) CrossRef
刊物类别:Physics and Astronomy
刊物主题:Physics Physics Mathematics Engineering, general Computer Science, general Characterization and Evaluation Materials
出版者:Springer Netherlands
ISSN:1573-1332
文摘
Entanglement witnesses are non-positive Hermitian operators which can detect whether a quantum state is entangled. Positive maps based on one and two given quantum states are constructed, and entanglement witnesses are generated by composing the positive maps with affine maps. An entanglement witness example is given at the end.