Skip to main content
SpringerLink
Log in

Analytic expressions of discord and geometric discord in Werner derivatives

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Ekert, A.: Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  7. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)

    Article  ADS  Google Scholar 

  8. Zhang, Z.J., Li, Y., Man, Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71, 044301 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Zhang, Z.J., Man, Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  11. Zhang, Z.J., Liu, Y.M.: Perfect teleportation of arbitrary n-qudit states using different quantum channels. Phys. Lett. A 372, 28 (2007)

    Article  ADS  MATH  Google Scholar 

  12. Cheung, C.Y., Zhang, Z.J.: Criterion for faithful teleportation with an arbitrary multiparticle channel. Phys. Rev. A 80, 022327 (2009)

    Article  ADS  Google Scholar 

  13. Ekert, A., Jozsa, R.: Quantum computation and shors factoring algorithm. Rev. Mod. Phys. 68, 733 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  14. Vedral, V., Plenio, M.B.: Basics of quantum computation. Prog. Quantum Electron. 22, 1 (1998)

    Article  ADS  Google Scholar 

  15. Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672 (1998)

    Article  ADS  Google Scholar 

  16. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  MATH  Google Scholar 

  17. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

  18. Luo, S.L.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

  19. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  20. Dakić, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  MATH  Google Scholar 

  21. Luo, S.L., Fu, S.S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  23. Madhok, V., Datta, A.: Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323 (2011)

    Article  ADS  Google Scholar 

  24. Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011)

    Article  ADS  MATH  Google Scholar 

  25. Dakić, B., Lipp, Y.O., Ma, X., et al.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012)

    Article  Google Scholar 

  26. Li, B., Fei, S.M., Wang, Z.X., Fan, H.: Assisted state discrimination without entanglement. Phys. Rev. A 85, 022328 (2012)

    Article  ADS  Google Scholar 

  27. Luo, S.L.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  28. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)

    Article  ADS  Google Scholar 

  29. Giorda, P., Paris, M.G.A.: Gaussian quantum discord. Phys. Rev. Lett. 105, 020503 (2010)

    Article  ADS  Google Scholar 

  30. Giorgi, G.L., Bellomo, B., Galve, F., Zambrini, R.: Genuine quantum and classical correlations in multipartite systems. Phys. Rev. Lett. 107, 190501 (2011)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  32. Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  46. Galve, F., Giorgi, G.L., Zambrini, R.: Orthogonal measurements are almost sufficient for quantum discord of two qubits. EPL 96, 40005 (2011)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  48. Chitambar, E.: Quantum correlations in high-dimensional states of high symmetry. Phys. Rev. A 86, 032110 (2012)

    Article  ADS  Google Scholar 

  49. Zhou, T., Cui, J., Long, G.L.: Measure of nonclassical correlation in coherence-vector representation. Phys. Rev. A 84, 062105 (2011)

    Article  ADS  Google Scholar 

  50. Hiroshima, T., Ishizaka, S.: Local and nonlocal properties of Werner states. Phys. Rev. A 62, 044302 (2000)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

Supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20103401110007, the National Natural Science Foundation of China under Grant Nos. 10975001 and 11375011, the Program for Excellent Talents at the University of Guangdong province (Guangdong Teacher Letter [1010] No. 79), and the 211 Project of Anhui University.

Author information

Authors and Affiliations

  1. School of Physics and Materials Science, Anhui University, Hefei, 230039, China

    Haojie Tang, Jianlan Chen, Biaoliang Ye & Zhanjun Zhang

  2. Department of Physics, Shaoguan University, Shaoguan, 512005, China

    Yimin Liu

Authors
  1. Haojie Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yimin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianlan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Biaoliang Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhanjun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhanjun Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tang, H., Liu, Y., Chen, J. et al. Analytic expressions of discord and geometric discord in Werner derivatives. Quantum Inf Process 13, 1331–1344 (2014). https://doi.org/10.1007/s11128-014-0731-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-014-0731-0

Keywords

Search

Navigation