Skip to main content
Springer Nature Link
Log in

Better quantum control does not imply better discrimination effect

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Quantum feedback control (QFBC) and quantum feedforward control (QFFC) are two major techniques for protecting quantum states against decoherence. Based on this, Guo et al. proposed a scheme by combining the QFFC and the minimum-error discrimination (MED) to realize a better effect of discriminating two non-orthogonal states after passing a noisy channel (Phys Rev A 91:022321, 2015) than the scheme without the QFFC. Recently, Cao et al. proposed a novel composite control scheme for protecting such states (Phys Rev A 95:032313, 2017), where QFBC and QFFC are combined. They showed that the performance of the composite control scheme is better than that of the previous control schemes in terms of the success probability and the fidelity. In this paper, we examine the discrimination scheme by combining the composite control and the MED and observe an interesting phenomenon, i.e., better quantum control does not imply better discrimination effect. Finally, we explain this phenomenon.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Bennett, C.H., Brassard, G.: In: Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing. IEEE, New York, p. 175 (1984)

  2. Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557–559 (1992)

    ADS  MathSciNet  MATH  Google Scholar 

  3. Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)

    ADS  MathSciNet  MATH  Google Scholar 

  4. Helstrom, C.W.: Quantum Detection and Estimation Theory, Mathematics in Science and Engineering, vol. 123. Academic, New York (1976)

    MATH  Google Scholar 

  5. Holevo, A.S.: Statistical decision theory for quantum systems. J. Multivar Anal. 3, 337–394 (1973)

    MathSciNet  MATH  Google Scholar 

  6. Yuen, H.P., Kenndey, R.S., Lax, M.: Optimum testing of multiple hypotheses in quantum detection theory. IEEE Trans. Inf. Theory 21, 125–134 (1975)

    MathSciNet  MATH  Google Scholar 

  7. Bergou, J.A.: Discrimination of quantum states. J. Mod. Opt. 57, 160–180 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  8. Barnett, S.M.: Minimum-error discrimination between multiply symmetric states. Phys. Rev. A 64, 030303 (2001)

    ADS  Google Scholar 

  9. Andersson, E., Barnett, S.M., Gilson, C.R., Hunter, K.: Minimum-error discrimination between three mirror-symmetric states. Phys. Rev. A 65, 052308 (2002)

    ADS  Google Scholar 

  10. Chou, C.L., Hsu, L.Y.: Minimum-error discrimination between symmetric mixed quantum states. Phys. Rev. A 68, 042305 (2003)

    ADS  Google Scholar 

  11. Herzog, U., Bergou, J.A.: Minimum-error discrimination between subsets of linearly dependent quantum states. Phys. Rev. A 65, 050305 (2002)

    ADS  Google Scholar 

  12. Ivanovic, I.D.: How to differentiate between non-orthogonal states. Phys. Lett. A 123, 257–259 (1987)

    ADS  MathSciNet  Google Scholar 

  13. Dieks, D.: Overlap and distinguishability of quantum states. Phys. Lett. A 126, 303–306 (1988)

    ADS  MathSciNet  Google Scholar 

  14. Peres, A.: How to differentiate between non-orthogonal states. Phys. Lett. A 128, 19 (1988)

    ADS  MathSciNet  Google Scholar 

  15. Jaeger, G., Shimony, A.: Optimal distinction between two non-orthogonal quantum states. Phys. Lett. A 197, 83–87 (1995)

    ADS  MathSciNet  MATH  Google Scholar 

  16. Peres, A., Terno, D.R.: Optimal distinction between two non-orthogonal quantum states. J. Phys. A: Math. Gen. 31, 7105–7111 (1998)

    ADS  MATH  Google Scholar 

  17. Zhang, C.W., Li, C.F., Guo, G.C.: General strategies for discrimination of quantum states. Phys. Lett. A 261, 25–29 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  18. Chefles, A., Barnett, S.M.: Optimum unambiguous discrimination between linearly independent symmetric states. Phys. Lett. A 250, 223–229 (1998)

    ADS  Google Scholar 

  19. Sun, Y., Bergou, J.A., Hillery, M.: Optimum unambiguous discrimination between subsets of nonorthogonal quantum states. Phys. Rev. A 66, 032315 (2002)

    ADS  Google Scholar 

  20. Eldar, Y.C.: A semidefinite programming approach to optimal unambiguous discrimination of quantum states. IEEE Trans. Inf. Theory 49, 446–456 (2003)

    MathSciNet  MATH  Google Scholar 

  21. Qiu, D.: Optimum unambiguous discrimination between subsets of quantum states. Phys. Lett. A 309, 189–197 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  22. Rudolph, T., Spekkens, R.W., Turner, P.S.: Unambiguous discrimination of mixed states. Phys. Rev. A 68, 010301 (2003)

    ADS  MathSciNet  Google Scholar 

  23. Feng, Y., Duan, R., Ying, M.: Unambiguous discrimination between mixed quantum states. Phys. Rev. A 70, 012308 (2004)

    ADS  Google Scholar 

  24. Raynal, P., Lütkenhaus, N., van Enk, S.J.: Reduction theorems for optimal unambiguous state discrimination of density matrices. Phys. Rev. A 68, 022308 (2003)

    ADS  Google Scholar 

  25. Herzog, U., Bergou, J.A.: Optimum unambiguous discrimination of two mixed quantum states. Phys. Rev. A 71, 050301 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  26. Raynal, P., Lütkenhaus, N.: Optimal unambiguous state discrimination of two density matrices: lower bound and class of exact solutions. Phys. Rev. A 72, 022342 (2005)

    ADS  Google Scholar 

  27. Bergou, J.A., Feldman, E., Hillery, M.: Optimal unambiguous discrimination of two subspaces as a case in mixed-state discrimination. Phys. Rev. A 73, 032107 (2006)

    ADS  MathSciNet  Google Scholar 

  28. Brańczyk, A.M., Mendonça, P.E.M.F., Gilchrist, A., Doherty, A.C., Bartlett, S.D.: Quantum control of a single qubit. Phys. Rev. A 75, 012329 (2007)

    ADS  MathSciNet  Google Scholar 

  29. Xiao, X., Feng, M.: Reexamination of the feedback control on quantum states via weak measurements. Phys. Rev. A 83, 054301 (2011)

    ADS  Google Scholar 

  30. Yang, Y., Zhang, X.Y., Ma, J., Yi, X.X.: Extended techniques for feedback control of a single qubit. Phys. Rev. A 87, 012333 (2013)

    ADS  Google Scholar 

  31. Jacobs, K.: Feedback control for communication with non-orthogonal states. Quantum Inf. Comput. 7, 127–138 (2007)

    MathSciNet  MATH  Google Scholar 

  32. Wang, C.-Q., Xu, B.M., Zou, J., He, Z., Yan, Y., Li, J.-G., Shao, B.: Feed-forward control for quantum state protection against decoherence. Phys. Rev. A 89, 032303 (2014)

    ADS  Google Scholar 

  33. Harraz, S., Cong, S., Li, K.: Two-qubit state recovery from amplitude damping based on weak measurement. eprint arXiv:1808.03094 (2018)

  34. Cao, Y., Tian, G., Zhang, Z.C., Yang, Y.H., Wen, Q.Y., Gao, F.: Composite control for protecting two nonorthogonal qubit states against decoherence. Phys. Rev. A 95, 032313 (2017)

    ADS  Google Scholar 

  35. Carvalho, A.R.R., Reid, A.J.S., Hope, J.J.: Controlling entanglement by direct quantum feedback. Phys. Rev. A 78, 012334 (2008)

    ADS  Google Scholar 

  36. Guo, L.S., Xu, B.M., Zou, J., Wang, C., Li, H., Li, J., Shao, B.: Discriminating two nonorthogonal states against a noise channel by feed-forward control. Phys. Rev. A 91, 022321 (2015)

    ADS  Google Scholar 

  37. Gillett, G.G., Dalton, R.B., Lanyon, B.P., Almeida, M.P., Barbieri, M., Pryde, G.J., O’Brien, J.L., Resch, K.J., Bartlett, S.D., White, A.G.: Experimental feedback control of quantum systems using weak measurements. Phys. Rev. Lett. 104, 080503 (2010)

    ADS  Google Scholar 

  38. Kim, Y.S., Lee, J.C., Kwon, O., Kim, Y.H.: Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117–120 (2012)

    Google Scholar 

  39. Solis-Prosser, M.A., Fernandes, M.F., Jimenez, O., Delgado, A., Neves, L.: Experimental minimum-error quantum-state discrimination in high dimensions. Phys. Rev. Lett. 118, 100501 (2017)

    ADS  Google Scholar 

  40. Li, J.Y., Ma, C.C., Zhang, K.J.: A novel lattice-based CP-ABPRE scheme for cloud sharing. Symmetry 11(10), 1262 (2019)

    Google Scholar 

  41. Zhang, K.J., Zhang, X., Jia, H.Y., Zhang, L.: A new n-party quantum secret sharing model based on multiparty entangled states. Quantum Inf. Process. 18(3), 21 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  42. Zhang, K.J., Zhang, L., Song, T.T., Yang, Y.H.: A potential application in quantum networks—deterministic quantum operation sharing schemes with Bell states. Sci. Chin. Phys. Mech. Astron. 59(6), 660302 (2016)

    Google Scholar 

  43. Zhang, L., Sun, H.W., Zhang, K.J., Jia, H.Y.: An improved arbitrated quantum signature protocol based on the key-controlled chained CNOT encryption. Quantum Inf. Process. 16(3), 70 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  44. Zhang, K.J., Kwek, L., Ma, C.G., Zhang, L., Sun, H.-W.: Security analysis with improved design of post-confirmation mechanism for quantum sealed-bid auction with single photons. Quantum Inf. Process. 17(2), 38 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  45. Zhang, L., Dong, S., Zhang, K.J.: A controller-independent quantum dialogue protocol with four-particle states. Int. J. Theor. Phys. 58(6), 1972–1936 (2019)

    MathSciNet  MATH  Google Scholar 

  46. Zhang, L., Li, S., Zhang, K.J., Sun, H.-W.: Cryptanalysis and improvement of some quantum proxy blind signature schemes. Int. J. Theor. Phys. 58(4), 1047–1059 (2019)

    MathSciNet  MATH  Google Scholar 

  47. Zhang, H.Y., Zhang, L., Zhang, K.J.: A new quantum proxy signature model based on a series of genuine entangled states. Int. J. Theor. Phys. 58(2), 591–604 (2019)

    MATH  Google Scholar 

  48. Zhang, L., Sun, H.-W., Zhang, K.J., Wang, Q.L., Cai, X.Q.: The security problems in some novel arbitrated quantum signature protocols. Int. J. Theor. Phys. 56(8), 2433–2444 (2017)

    MATH  Google Scholar 

  49. Zhang, L., Zhang, H.Y., Zhang, K.J., Wang, Q.L.: The security analysis and improvement of some novel quantum proxy signature schemes. Int. J. Theor. Phys. 56(6), 1983–1994 (2017)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61572053); Beijing Natural Science Foundation (Grant No. 4182006); and Guangxi Key Laboratory of Cryptography and Information Security (Grant No. GCIS201810).

Author information

Authors and Affiliations

  1. Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, China

    Yu-Guang Yang, Ning Chen, Yong-Li Yang, Yi-Hua Zhou & Wei-Min Shi

  2. Beijing Key Laboratory of Trusted Computing, Beijing, 100124, China

    Yu-Guang Yang

Authors
  1. Yu-Guang Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Ning Chen
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Yong-Li Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Yi-Hua Zhou
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Wei-Min Shi
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yu-Guang Yang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, YG., Chen, N., Yang, YL. et al. Better quantum control does not imply better discrimination effect. Quantum Inf Process 19, 168 (2020). https://doi.org/10.1007/s11128-020-02667-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02667-9

Keywords