Analytic expressions of discord and geometric discord in Werner derivatives

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• 作者：Haojie Tang (1)
  Yimin Liu (2)
  Jianlan Chen (1)
  Biaoliang Ye (1)
  Zhanjun Zhang (1)
  
• 关键词：Quantum discord ; Geometric discord ; Werner derivative
• 刊名：Quantum Information Processing
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：13
• 期：6
• 页码：1331-1344
• 全文大小：
• 参考文献：1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935) CrossRef
  2. Ekert, A.: Quantum cryptography based on bell鈥檚 theorem. Phys. Rev. Lett. 67, 661 (1991) CrossRef
  3. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992) CrossRef
  4. Bennett, C.H., Brassard, G., Crepeau, C., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993) CrossRef
  5. Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001) CrossRef
  6. Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003) CrossRef
  7. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004) CrossRef
  8. Zhang, Z.J., Li, Y., Man, Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71, 044301 (2005) CrossRef
  9. Zhang, Z.J., Man, Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005) CrossRef
  10. Yu, C.S., Song, H.S., Wang, Y.H.: Remote preparation of a qudit using maximally entangled states of qubits. Phys. Rev. A 73, 022340 (2006) CrossRef
  11. Zhang, Z.J., Liu, Y.M.: Perfect teleportation of arbitrary n-qudit states using different quantum channels. Phys. Lett. A 372, 28 (2007) CrossRef
  12. Cheung, C.Y., Zhang, Z.J.: Criterion for faithful teleportation with an arbitrary multiparticle channel. Phys. Rev. A 80, 022327 (2009) CrossRef
  13. Ekert, A., Jozsa, R.: Quantum computation and shors factoring algorithm. Rev. Mod. Phys. 68, 733 (1996) CrossRef
  14. Vedral, V., Plenio, M.B.: Basics of quantum computation. Prog. Quantum Electron. 22, 1 (1998) CrossRef
  15. Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672 (1998) CrossRef
  16. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001) CrossRef
  17. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008) CrossRef
  18. Luo, S.L.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008) CrossRef
  19. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010) CrossRef
  20. Daki膰, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010) CrossRef
  21. Luo, S.L., Fu, S.S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010) CrossRef
  22. Girolami, D., Paternostro, M., Adesso, G.: Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states. J. Phys. A: Math. Theor. 44, 352002 (2011) CrossRef
  23. Madhok, V., Datta, A.: Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323 (2011) CrossRef
  24. Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011) CrossRef
  25. Daki膰, B., Lipp, Y.O., Ma, X., et al.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012) CrossRef
  26. Li, B., Fei, S.M., Wang, Z.X., Fan, H.: Assisted state discrimination without entanglement. Phys. Rev. A 85, 022328 (2012) CrossRef
  27. Luo, S.L.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008) CrossRef
  28. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010) CrossRef
  29. Giorda, P., Paris, M.G.A.: Gaussian quantum discord. Phys. Rev. Lett. 105, 020503 (2010) CrossRef
  30. Giorgi, G.L., Bellomo, B., Galve, F., Zambrini, R.: Genuine quantum and classical correlations in multipartite systems. Phys. Rev. Lett. 107, 190501 (2011) CrossRef
  31. Li, B., Wang, Z.X., Fei, S.M.: Quantum discord and geometry for a class of two-qubit states. Phys. Rev. A 83, 022321 (2011) CrossRef
  32. Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011) CrossRef
  33. Ye, B.L., Liu, Y.M., Chen, J.L., Liu, X.S., Zhang, Z.J.: Analytic expressions of quantum correlations in qutrit Werner states. Quantum Inf. Process. 12, 2355 (2013) CrossRef
  34. Ye, B.L., Liu, Y.M., Liu, X.S., Zhang, Z.J.: Quantum correlations in a family of bipartite qubit-qutrit separable states. Chin. Phys. Lett. 30, 020302 (2013) CrossRef
  35. Ye, B.L., Liu, Y.M., Xu, C.J., Liu, X.S., Zhang, Z.J.: Quantum correlations in a family of two-qubit separable states. Commun. Theor. Phys. (in press)
  36. Wang, S.F., Liu, Y.M., Li, G.F., Liu, X.S., Zhang, Z.J.: Quantum discord in any mixture of two bi-qubit arbitrary product states. Commun. Theor. Phys. (in press)
  37. Zhang, Z.J., Ye, B.L., Fei, S.M.: quant-ph/1206.0221
  38. Zhang, Z.J.: quant-ph/1202.3640
  39. Wei, H.R., Ren, B.C., Deng, F.G.: Geometric measure of quantum discord for a two-parameter class of states in a qubit-qutrit system under various dissipative channels. Quantum Inf. Process. 12, 1109 (2013) CrossRef
  40. Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008) CrossRef
  41. Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: Robustness of quantum discord to sudden death. Phys. Rev. A 80, 024103 (2009) CrossRef
  42. Xu, J.S., Xu, X.Y., Li, C.F., Zhang, C.J., Zou, X.B., Guo, G.C.: Experimental investigation of classical and quantum correlations under decoherence. Nat. Commun. 1, 7 (2010)
  43. Lu, X.M., Ma, J., Xi, Z.J., Wang, X.G.: Optimal measurements to access classical correlations of two-qubit states. Phys. Rev. A 83, 012327 (2011) CrossRef
  44. Hu, X.Y., Gu, Y., Gong, Q., Guo, G.C.: Necessary and sufficient condition for Markovian-dissipative-dynamics-induced quantum discord. Phys. Rev. A 84, 022113 (2011) CrossRef
  45. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012) CrossRef
  46. Galve, F., Giorgi, G.L., Zambrini, R.: Orthogonal measurements are almost sufficient for quantum discord of two qubits. EPL 96, 40005 (2011) CrossRef
  47. Shi, M., Sun, C., Jiang, F., Yan, X., Du, J.: Optimal measurement for quantum discord of two-qubit states. Phys. Rev. A 85, 064104 (2012) CrossRef
  48. Chitambar, E.: Quantum correlations in high-dimensional states of high symmetry. Phys. Rev. A 86, 032110 (2012) CrossRef
  49. Zhou, T., Cui, J., Long, G.L.: Measure of nonclassical correlation in coherence-vector representation. Phys. Rev. A 84, 062105 (2011) CrossRef
  50. Hiroshima, T., Ishizaka, S.: Local and nonlocal properties of Werner states. Phys. Rev. A 62, 044302 (2000) CrossRef
  
• 作者单位：Haojie Tang (1)
  Yimin Liu (2)
  Jianlan Chen (1)
  Biaoliang Ye (1)
  Zhanjun Zhang (1)
  
  1. School of Physics and Materials Science, Anhui University, Hefei, 230039, China
  2. Department of Physics, Shaoguan University, Shaoguan, 512005, China
  
• ISSN：1573-1332

文摘

Werner derivatives are a special kind of mixing states transformed from Werner states by unitary operations (Hiroshima and Ishizaka in Phys Rev A 62:044302, 2000). In this paper, the inherent quantum correlations in Werner derivatives are quantified by two different quantifiers, i.e., quantum discord and geometric discord. Different analytic expressions of the two discords in Werner derivatives are derived out. Some distinct features of the discords and their underlying physics are exposed via discussions and analyses. Moreover, it is found that the amount of quantum correlations quantified by either quantifier in each derivative cannot exceed that in the original Werner state. In other words, no unitary operation can increase quantum correlation in a Werner state as far as the two quantifiers are concerned.