Analytic expression of quantum correlations in qutrit Werner states undergoing local and nonlocal unitary operations

详细信息    查看全文

• 作者：Guofeng Li (1)
  Yimin Liu (2)
  Haojie Tang (1)
  Xiaofeng Yin (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
  
• 关键词：Quantum correlation ; Quantum discord ; Measurement ; induced disturbance ; Qutrit Werner states ; Local individual and nonlocal collective unitary operations
• 刊名：Quantum Information Processing
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：14
• 期：2
• 页码：559-572
• 全文大小：992 KB
• 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鈥揚odolsky鈥揜osen 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鈥揚odolsky鈥揜osen 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鈥揚odolsky鈥揜osen 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., Man, Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005) CrossRef
  9. Zhang, Z.J., Liu, Y.M.: Perfect teleportation of arbitrary n-qudit states using different quantum channels. Phys. Lett. A 372, 28 (2007) CrossRef
  10. Cheung, C.Y., Zhang, Z.J.: Criterion for faithful teleportation with an arbitrary multiparticle channel. Phys. Rev. A 80, 022327 (2009) CrossRef
  11. 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
  12. Ekert, A., Jozsa, R.: Quantum computation and Shor鈥檚 factoring algorithm. Rev. Mod. Phys. 68, 733 (1996) CrossRef
  13. Vedral, V., Plenio, M.B.: Basics of quantum computation. Prog. Quantum Electron. 22, 1 (1998) CrossRef
  14. Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672 (1998) CrossRef
  15. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008) CrossRef
  16. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001) CrossRef
  17. Madhok, V., Datta, A.: Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323 (2011) CrossRef
  18. Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011) CrossRef
  19. Daki膰, B., Lipp, Y.O., Ma, X., et al.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012) CrossRef
  20. Li, B., Fei, S.M., Wang, Z.X., Fan, H.: Assisted state discrimination without entanglement. Phys. Rev. A 85, 022328 (2012) CrossRef
  21. Luo, S.L.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008) CrossRef
  22. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010) CrossRef
  23. Daki膰, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010) CrossRef
  24. Luo, S.L.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008) CrossRef
  25. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010) CrossRef
  26. Huang, Y.C.: Quantum discord for two-qubit X states: analytical formula with very small worst-case error. Phys. Rev. A 88, 014302 (2013) CrossRef
  27. Huang, Y.C.: Scaling of quantum discord in spin models. Phys. Rev. B 89, 054410 (2014) CrossRef
  28. Huang, Y.C.: Computing quantum discord is NP-complete. New J. Phys. 16, 033027 (2014) CrossRef
  29. Giorda, P., Paris, M.G.A.: Gaussian quantum discord. Phys. Rev. Lett. 105, 020503 (2010) CrossRef
  30. Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011) CrossRef
  31. 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
  32. Ye, B.L., Liu, Y.M., Liu, X.S., Zhang, Z.J.: Quantum correlations in a family of bipartite qubit鈥搎utrit separable states. Chin. Phys. Lett. 30, 020302 (2013) CrossRef
  33. Zhang, Z.J., Ye, B.L., Fei, S.M.: quant-ph/1206.0221.
  34. Zhang, Z.J.: quant-ph/1202.3640.
  35. Tang, H., Liu, Y.M., Chen, J., Ye, B., Zhang, Z.J.: Analytic expressions of discord and geometric discord in Werner derivatives. Quantum Inf. Process. 14, 1331 (2014) CrossRef
  36. Wei, H.R., Ren, B.C., Deng, F.G.: Geometric measure of quantum discord for a two-parameter class of states in a qubit鈥搎utrit system under various dissipative channels. Quantum Inf. Process. 12, 1109 (2013) CrossRef
  37. Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008) CrossRef
  38. Werlang, T., Souza, S., Fanchini, F.F.: Robustness of quantum discord to sudden death. Phys. Rev. A 80, 024103 (2009) CrossRef
  39. 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
  40. Aharon, B., Daniel, R.T.: Quantum discord, local operations, and Maxwells demons. Phys. Rev. A 81, 062103 (2010) CrossRef
  41. Auccaise, R., C茅leri, L.C., Soares-Pinto, D.O., deAzevedo, E.R., Maziero, J., Souza, A.M., Bonagamba, T.J., Sarthour, R.S., Oliveira, I.S., Serra, R.M.: Environment-induced sudden transition in quantum discord dynamics. Phys. Rev. Lett. 107, 140403 (2011) CrossRef
  42. Streltsov, A., Kampermann, H., Bru脽, D.: Behavior of quantum correlations under local noise. Phys. Rev. Lett. 107, 170502 (2011) CrossRef
  43. Gessner, M., Breuer, H.: Detecting nonclassical system-environment correlations by local operations. Phys. Rev. Lett. 107, 180402 (2011) CrossRef
  44. Francesco, C., Vittorio, G.: Creating quantum correlations through local nonunitary memoryless channels. Phys. Rev. A 85, 010102 (2012) CrossRef
  45. Hu, X., Fan, H., Zhou, D.L., Liu, W.M.: Quantum correlating power of local quantum channels. Phys. Rev. A 87, 032340 (2013) CrossRef
  46. Lanyon, B.P., Jurcevic, P., Hempel, C., Gessner, M., Vedral, V., Blatt, R., Roos, C.F.: Experimental generation of quantum discord via noisy processes. Phys. Rev. Lett. 111, 100504 (2013) 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. Xie, C.M., Liu, Y.M., Li, G.F., Zhang, Z.J.: A note on quantum correlations in Werner states under two collective noises. Quantum Inf. Process. 13, 2713 (2014)
  51. Xie, C., Liu, Y., Xing, H., Chen, J., Zhang, Z.: Quantum correlation swapping. Quantum Inf. Process. (2014). doi:10.1007/s11128-014-0875-y
  52. Bronzan, J.B.: Parametrization of SU(3). Phys. Rev. D 38, 1994 (1988) 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

Quantum correlations of a qutrit pair in Werner states undergoing local and nonlocal unitary operations are quantified in terms of two different methods, i.e., quantum discord (Ollivier and Zurek in Phys Rev Lett 88:017901, 2001) and measurement-induced disturbance (Luo in Phys Rev A 77:022301, 2008). Analytic expressions of the two kinds of quantum correlations in the system are worked on and found to be completely the same. By virtue of investigations and discussions, we expose some distinct features of the correlations and their underlying physics. More importantly, we found that both local and nonlocal unitary operations cannot increase quantum correlation in a qutrit Werner state for the two quantifiers which are concerned.