Analytic expressions of quantum correlations in qutrit Werner states

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• 作者：Biaoliang Ye (1)
  Yimin Liu (2)
  Jianlan Chen (1)
  Xiansong Liu (1)
  Zhanjun Zhang (1)
  
• 关键词：Quantum correlations ; Analytic expressions ; Qutrit Werner states ; Five methods
• 刊名：Quantum Information Processing
• 出版年：2013
• 出版时间：July 2013
• 年：2013
• 卷：12
• 期：7
• 页码：2355-2369
• 全文大小：234KB
• 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. Bohr, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48, 696 (1935) CrossRef
  3. Ekert, A.: Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67, 661 (1991) 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. 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
  6. Zhou, J.D., Hou, G., Zhang, Y.D.: Teleportation scheme of S-level quantum pure states by two-level Einstein-Podolsky-Rosen states. Phys. Rev. A 64, 012301 (2001) CrossRef
  7. Zhang, Z.J., Liu, Y.M.: Perfect teleportation of arbitrary n-qudit states using different quantum channels. Phys. Lett. A 372, 28 (2007) CrossRef
  8. Cheung, C.Y., Zhang, Z.J.: Criterion for faithful teleportation with an arbitrary multiparticle channel. Phys. Rev. A 80, 022327 (2009) CrossRef
  9. Hillery, M., Bu?ek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999) CrossRef
  10. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004) CrossRef
  11. Zhang, Z.J., Man, Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005) CrossRef
  12. Zhang, Z.J., Li, Y., Man, Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71, 044301 (2005) CrossRef
  13. Yan, F.L., Gao, T.: Quantum secret sharing between multiparty and multiparty without entanglement. Phys. Rev. A 72, 012304 (2005) CrossRef
  14. Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001) CrossRef
  15. Zeng, B., Zhang, P.: Remote-state preparation in higher dimension and the parallelizable manifold $S^{n-1}$ . Phys. Rev. A 65, 022316 (2002) CrossRef
  16. 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
  17. Vidal, G.: Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91, 147902 (2003) CrossRef
  18. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001) CrossRef
  19. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008) CrossRef
  20. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008) CrossRef
  21. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010) CrossRef
  22. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008) CrossRef
  23. Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008) CrossRef
  24. 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)
  25. Madhok, V., Datta, A.: Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323 (2011) CrossRef
  26. Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011) CrossRef
  27. Daki?, B., Lipp, Y.O., Ma, X., et al.: Quantum discord as resource for remote state preparation. Nature Phys. 8, 666 (2012) CrossRef
  28. Li, B., Fei, S.M., Wang, Z.X., Fan, H.: Assisted state discrimination without entanglement. Phys. Rev. A 85, 022328 (2012) CrossRef
  29. 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
  30. 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
  31. 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
  32. Lu, X.M., Ma, J., Xi, Z., Wang, X.: Optimal measurements to access classical correlations of two-qubit states. Phys. Rev. A 83, 012327 (2011) CrossRef
  33. Lu, X.M., Xi, Z., Sun, Z., Wang, X.: Geometric measure of quantum discord under decoherence. Quantum Inf. Comput. 10, 0994 (2010)
  34. Li, B., Wang, Z.X., Fei, S.M.: Geometry for a class of two-qubit states. Phys. Rev. A 83, 022321 (2011) CrossRef
  35. 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
  36. Luo, S., Fu, S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010) CrossRef
  37. 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)
  38. Zhou, T., Cui, J., Long, G.L.: Measure of nonclassical correlation in coherence-vector representation. Phys. Rev. A 84, 062105 (2011) CrossRef
  39. Zhang, Z.J., Ye, B.L., Fei, S.M.: quant-ph/1206.0221
  40. Zhang, Z.J.: quant-ph/1202.3640
  41. 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
  42. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010) CrossRef
  43. Daki?, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010) CrossRef
  44. Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011) CrossRef
  45. Giorgi, G.L., Bellomo, B., Galve, F., Zambrini, R.: Genuine quantum and classical correlations in multipartite systems. Phys. Rev. Lett. 107, 190501 (2011) CrossRef
  46. Giorda, P., Paris, M.G.A.: Gaussian quantum discord. Phys. Rev. Lett. 105, 020503 (2010) CrossRef
  47. Baumgartner, B., Hiesmayr, B.C., Narnhofer, H.: State space for two qutrits has a phase space structure in its core. Phys. Rev. A 74, 032327 (2006) CrossRef
  48. Derkacz, L., Jakobczyk, L.: Entanglement versus entropy for a class of mixed two-qutrit states. Phys. Rev. A 76, 042304 (2007) CrossRef
  49. Bronzan, J.B.: Parametrization of SU(3). Phys. Rev. D 38, 1994 (1988) CrossRef
  50. Piani, M.: Problem with geometric discord. Phys. Rev. A 86, 034101 (2012) CrossRef
  51. Galve, F., Giorgi, G.L., Zambrini, R.: Orthogonal measurements are almost sufficient for quantum discord of two qubits. EPL 96, 40005 (2011) CrossRef
  
• 作者单位：Biaoliang Ye (1)
  Yimin Liu (2)
  Jianlan Chen (1)
  Xiansong Liu (1)
  Zhanjun Zhang (1)
  
  1. School of Physics and Material Science, Anhui University, Hefei, 230039, Anhui, China
  2. Department of Physics, Shaoguan University, Shaoguan, 512005, China
  
• ISSN：1573-1332

文摘

Quantum correlations in qutrit Werner states are extensively investigated with five popular methods, namely, original quantum discord (OQD) (Ollivier and Zurek in Phys Rev Lett 88:017901, 2001), measurement-induced disturbance (MID) (Luo in Phys Rev A 77:022301, 2008), ameliorated MID (AMID) (Girolami et al. in J Phys A Math Theor 44:352002, 2011), relative entropy (RE) (Modi et al. in Phys Rev Lett 104:080501, 2010) and geometric discord (GD) (Daki? et al. in Phys Rev Lett 105:190502, 2010). Two different analytic expressions of quantum correlations are derived. Quantum correlations captured by the former four methods are same and bigger than those obtained via the GD method. Nonetheless, they all qualitatively characterize quantum correlations in the concerned states. Moreover, as same as the qubit case, there exist quantum correlations in separable qutrit Werner states, too.