Log in

Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Recently, the method that using an entanglement as a resource to distinguish orthogonal product states by local operations and classical communication (LOCC) has brought into focus. Zhang et al. (Sci Rep 6:30493, 2016) presented protocols which use an entanglement to distinguish some classes of orthogonal product states in \(\mathbb {C}^m\otimes \mathbb {C}^n\). In this paper, we mainly study the local distinguishability of multipartite product states. For the class of locally indistinguishable multipartite product states constructed by Wang et al. (Quantum Inf Process 16:5, 2017), we present a protocol that distinguishes perfectly these quantum states by LOCC using an entangled state as a resource for implementing quantum measurements.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Ghosh, S., Kar, G., Roy, A., Sen, A., Sen, U.: Distinguishability of Bell states. Phys. Rev. Lett. 87, 277902 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  2. Ghosh, S., Kar, G., Roy, A., Sarkar, D.: Distinguishability of maximally entangled states. Phys. Rev. A 70, 022304 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Hayashi, M., Markham, D., Murao, M., Owari, M., Virmani, S.: Bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication. Phys. Rev. Lett. 96, 040501 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  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)

    Article  ADS  MathSciNet  Google Scholar 

  5. Walgate, J., Hardy, L.: Nonlocality, asymmetry, and distinguishing bipartite states. Phys. Rev. Lett. 89, 147901 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Horodecki, M., Sen, A., Sen, U., Horodecki, K.: Local indistinguishability: more nonlocality with less entanglement. Phys. Rev. Lett. 90, 047902 (2003)

    Article  ADS  Google Scholar 

  7. De Rinaldis, S.: Distinguishability of complete and unextendible product bases. Phys. Rev. A 70, 022309 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Nathanson, M.: Distinguishing bipartitite orthogonal states using LOCC: best and worst cases. J. Math. Phys. 46, 062103 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Niset, J., Cerf, N.J.: Multipartite nonlocality without entanglement in many dimensions. Phys. Rev. A 74, 052103 (2006)

    Article  ADS  Google Scholar 

  10. Feng, Y., Shi, Y.: Characterizing locally indistinguishable orthogonal product states. IEEE Trans. Inf. Theory 55, 2799–2806 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Duan, R., **n, Y., Ying, M.: Locally indistinguishable subspaces spanned by three-qubit unextendible product bases. Phys. Rev. A 81, 032329 (2010)

    Article  ADS  Google Scholar 

  12. Childs, A.M., Leung, D., Mančinska, L., Ozols, M.: A framework for bounding nonlocality of state discrimination. Commun. Math. Phys. 323, 1121–1153 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Zhang, Z.C., Gao, F., Tian, G.J., Cao, T.Q., Wen, Q.Y.: Nonlocality of orthogonal product basis quantum states. Phys. Rev. A 90, 022313 (2014)

    Article  ADS  Google Scholar 

  14. Wang, Y.L., Li, M.S., Zheng, Z.J., Fei, S.M.: Nonlocality of orthogonal product-basis quantum states. Phys. Rev. A 92, 032313 (2015)

    Article  ADS  Google Scholar 

  15. Zhang, Z.C., Gao, F., Qin, S.J., Yang, Y.H., Wen, Q.Y.: Nonlocality of orthogonal product states. Phys. Rev. A 92, 012332 (2015)

    Article  ADS  Google Scholar 

  16. Zhang, Z.C., Gao, F., Cao, Y., Qin, S.J., Wen, Q.Y.: Local indistinguishability of orthogonal product states. Phys. Rev. A 93, 012314 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  17. Xu, G.B., Yang, Y.H., Wen, Q.Y., Qin, S.J., Gao, F.: Constructing locally indistinguishable orthogonal product bases in an \( m\otimes n \) system(2015). ar**v:1512.06485

  18. Xu, G.B., Wen, Q.Y., Qin, S.J., Yang, Y.H., Gao, F.: Quantum nonlocality of multipartite orthogonal product states. Phys. Rev. A 93, 032341 (2016)

    Article  ADS  Google Scholar 

  19. Wang, Y.L., Li, M.S., Zheng, Z.J., Fei, S.M.: The local indistinguishability of multipartite product states. Quantum Inf. Process. 16, 5 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Zhang, X., Weng, J., Tan, X., Luo, W.: Indistinguishability of pure orthogonal product states by LOCC. Quantum Inf. Process. 16, 168 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Zhang, Z.C., Zhang, K.J., Gao, F., Wen, Q.Y., Oh, C.H.: Construction of nonlocal multipartite quantum states. Phys. Rev. A 95, 052344 (2017)

    Article  ADS  Google Scholar 

  22. Cohen, S.M.: Understanding entanglement as resource: locally distinguishing unextendible product bases. Phys. Rev. A 77, 012304 (2008)

    Article  ADS  Google Scholar 

  23. Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  MATH  Google Scholar 

  25. Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  26. Kim, Y.H., Kulik, S.P., Shih, Y.: Quantum teleportation of a polarization state with a complete Bell state measurement. Phys. Rev. Lett. 86, 1370 (2001)

    Article  ADS  Google Scholar 

  27. Wang, C., Deng, F.G., Long, G.L.: Multi-step quantum secure direct communication using multi-particle Green–Horne–Zeilinger state. Opt. Commun. 253, 15–20 (2005)

    Article  ADS  Google Scholar 

  28. Tian-Yin, W., Su-Juan, Q., Qiao-Yan, W., Fu-Chen, Z.: Analysis and improvement of multiparty controlled quantum secure direct communication protocol. Acta. Physica Sinica. 57(12), 135–137 (2008)

    Google Scholar 

  29. Yang, C.W., Tsai, C.W., Hwang, T.: Fault tolerant two-step quantum secure direct communication protocol against collective noises. Sci. China Phys. 54, 496–501 (2011)

    Article  Google Scholar 

  30. Zhang, Z.C., Gao, F., Cao, T.Q., Qin, S.J., Wen, Q.Y.: Entanglement as a resource to distinguish orthogonal product states. Sci. Rep. 6, 30493 (2016)

    Article  ADS  Google Scholar 

  31. Bandyopadhyay, S., Halder, S., Nathanson, M.: Entanglement as a resource for local state discrimination in multipartite systems. Phys. Rev. A 94, 022311 (2016)

    Article  ADS  Google Scholar 

  32. Li, Z.G., Zhao, M., Li, S.M., Wang, H., Liu, W.M.: Maximally entangled state can be a mixed state. Quant. Inf. Comput 12, 0063–0073 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to **-Lin Tang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, HQ., **g, Nh. & Tang, XL. Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource. Quantum Inf Process 17, 195 (2018). https://doi.org/10.1007/s11128-018-1962-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1962-2

Keywords

Navigation