Bound on local unambiguous discrimination between multipartite quantum states

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• 作者：Ying-Hui Yang (1) (2)
  Fei Gao (1)
  Guo-Jing Tian (1)
  Tian-Qing Cao (1)
  Hui-Juan Zuo (1) (3)
  Qiao-Yan Wen (1)
  
  1. State Key Laboratory of Networking and Switching Technology ; Beijing University of Posts and Telecommunications ; Beijing ; 100876 ; China
  2. School of Mathematics and Information Science ; Henan Polytechnic University ; Jiaozuo ; 454000 ; China
  3. Mathematics and Information Science College ; Hebei Normal University ; Shijiazhuang ; 050024 ; China
  
• 关键词：Quantum information ; Upper bound ; Unambiguous discrimination ; Local operations and classical communication ; Multipartite quantum states
• 刊名：Quantum Information Processing
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：14
• 期：2
• 页码：731-737
• 全文大小：120 KB
• 参考文献：1. Roa, L., Retamal, J.C., Alid-Vaccarezza, M.: Dissonance is required for assisted optimal state discrimination. Phys. Rev. Lett. 107, 080401 (2011) CrossRef
  2. Zhang, F.L., Chen, J.L., Kwek, L.C., Vedral, V.: Requirement of dissonance in assisted optimal state discrimination. Sci. Rep. 3, 2134 (2013)
  3. Xu, L.F., Zhang, F.L., Liang, M.L., Chen, J.L.: Assisted optimal state discrimination without entanglement. Europhys. Lett. 106, 50004 (2014)
  4. Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070 (1999) CrossRef
  5. Walgate, J., Short, A.J., Hardy, L., Vedral, V.: Local distinguishability of multipartite orthogonal quantum states. Phys. Rev. Lett. 85, 4972 (2000) CrossRef
  6. Walgate, J., Hardy, L.: Nonlocality, asymmetry, and distinguishing bipartite states. Phys. Rev. Lett. 89, 147901 (2002) CrossRef
  7. Horodecki, M., Sen(De), A., Sen, U., Horodecki, K.: Local indistinguishability: more nonlocality with less entanglement. Phys. Rev. Lett. 90, 047902 (2003) CrossRef
  8. Watrous, J.: Bipartite subspaces having no bases distinguishable by local operations and classical communication. Phys. Rev. Lett. 95, 080505 (2005) CrossRef
  9. Duan, R., Feng, Y., Xin, Y., Ying, M.: Distinguishability of quantum states by separable operations. IEEE Trans. Inf. Theory 55, 1320 (2009) CrossRef
  10. Duan, R., Xin, Y., Ying, M.: Locally indistinguishable subspaces spanned by three-qubit unextendible product bases. Phys. Rev. A 81, 032329 (2010) CrossRef
  11. Yu, N., Duan, R., Ying, M.: Any \(2 \otimes n\) subspace is locally distinguishable. Phys. Rev. A 84, 012304 (2011) CrossRef
  12. Feng, Y., Shi, Y.: Characterizing locally indistinguishable orthogonal product states. IEEE Trans. Inf. Theory 55, 2799 (2009) CrossRef
  13. Yu, N., Duan, R., Ying, M.: Four locally indistinguishable ququad-ququad orthogonal maximally entangled states. Phys. Rev. Lett. 109, 020506 (2012) CrossRef
  14. Yang, Y., Gao, F., Tian, G., Cao, T., Wen, Q.: Local distinguishability of orthogonal quantum states in a \(2\otimes 2\otimes 2\) system. Phys. Rev. A 88, 024301 (2013) CrossRef
  15. Zhang, Z., Wen, Q., Gao, F., Tian, G., Cao, T.: One-way LOCC indistinguishability of maximally entangled states. Quantum Inf. Process. 13, 795C804 (2014)
  16. Chen, Y., Yang, D.: Optimal conclusive discrimination of two nonorthogonal pure product multipartite states through local operations. Phys. Rev. A 64, 064303 (2001) CrossRef
  17. Chen, Y., Yang, D.: Optimally conclusive discrimination of nonorthogonal entangled states by local operations and classical communications. Phys. Rev. A 65, 022320 (2002) CrossRef
  18. Ji, Z., Cao, H., Ying, M.: Optimal conclusive discrimination of two states can be achieved locally. Phys. Rev. A 71, 032323 (2005) CrossRef
  19. Chefles, A.: Condition for unambiguous state discrimination using local operations and classical communication. Phys. Rev. A 69, 050307 (2004) CrossRef
  20. Duan, R., Feng, Y., Ji, Z., Ying, M.: Distinguishing arbitrary multipartite basis unambiguously using local operations and classical communication. Phys. Rev. Lett. 98, 230502 (2007) CrossRef
  21. Bandyopadhyay, S., Walgate, J.: Local distinguishability of any three quantum states. J. Phys. A Math. Theor. 42, 072002 (2009) CrossRef
  22. Chitambar, E., Duan, R., Hsieh, M.H.: When do local operations and classical communication suffice for two-qubit state discrimination? IEEE Trans. Inf. Theory 60, 1549 (2014) CrossRef
  23. Duan, R.: Private communication
  
• 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

We investigate the upper bound on unambiguous discrimination by local operations and classical communication. We demonstrate that any set of linearly independent multipartite pure quantum states can be locally unambiguously discriminated if the number of states in the set is no more than \(\max \{d_{i}\}\) , where the space spanned by the set can be expressed in the irreducible form \(\otimes _{i=1}^{N}d_{i}\) and \(d_{i}\) is the optimal local dimension of the \(i\hbox {th}\) party. That is, \(\max \{d_{i}\}\) is an upper bound. We also show that it is tight, namely there exists a set of \(\max \{d_{i}\}+1\) states, in which at least one of the states cannot be locally unambiguously discriminated. Our result gives the reason why the multiqubit system is the only exception when any three quantum states are locally unambiguously distinguished.