Skip to main content
SpringerLink
Log in

Applications of quantum coherence via skew information under mutually unbiased bases

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The complementarity (upper bound) and uncertainty relations (lower bound) of the coherence via skew information under mutually unbiased bases (MUBs) are studied. The complementarity relation for the geometric measure of coherence is also obtained based on the relation between the coherence via skew information and the geometric measure of coherence. As applications, two tighter upper bounds are presented on the minimum error probabilities that discriminate a set of pure states with the least square measurement, which improve the results of Xiong et al. (Phys Rev A 98:032324, 2018).

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

Similar content being viewed by others

References

  1. Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)

    Article  ADS  Google Scholar 

  2. Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett 115, 020403 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  3. Xiong, C.H., Kumar, A., Wu, J.D.: Family of coherence measures and duality between quantum coherence and path distinguishability. Phys. Rev. A 98, 032324 (2018)

    Article  ADS  Google Scholar 

  4. Yu, C.S.: Quantum coherence via skew information and its polygamy. Phys. Rev. A 95, 042337 (2017)

    Article  ADS  Google Scholar 

  5. Rastegin, A.E.: Quantum-coherence quantifiers based on the Tsallis relative \(\alpha \)-entropies. Phys. Rev. A 93, 032136 (2016)

    ADS  Google Scholar 

  6. Hillery, M.: Coherence as a resource in decision problems: the Deutsch–Jozsa Algorithm and a variation. Phys. Rev. A. 93, 012111 (2016)

    Article  ADS  Google Scholar 

  7. Matera, J.M., Egloff, D., Killoran, N., Plenio, M.B.: Coherent control of quantum systems as a resource theory. Quantum Sci. Technol. 1, 01LT01 (2016)

  8. Giovannetti, V., Lloyd, S.: Advances in quantum metrology. Nat. Photon. 5, 222 (2011)

    Article  ADS  Google Scholar 

  9. Lostaglio, M., Jennings, D., Rudolph, T.: Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat. Commun. 6, 6383 (2015)

    Article  ADS  Google Scholar 

  10. Lostaglio, M., Korzekwa, K., Jennings, D., Rudolph, T.: Quantum coherence, time-translation symmetry, and thermodynamics. Phys. Rev. X 5, 021001 (2015)

    Google Scholar 

  11. Wang, Y., Tang, J., Wei, Z., Yu, S., Ke, Z., Xu, X., Li, C., Guo, G.: Directly measuring the degree of quantum coherence using interference fringes Phys. Phys. Rev. Lett. 118, 020403 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  12. Cheng, S.M., Hall, M.J.W.: Complementarity relations for quantum coherence. Phys. Rev. A. 92, 042101 (2015)

    Article  ADS  Google Scholar 

  13. Wang, Y.K., Ge, L.Z., Tao, Y.H.: Quantum coherence in mutually unbiased bases. Quant. Inf. Proc. 18, 164 (2019)

    Article  MathSciNet  Google Scholar 

  14. Spehner, D., Orszag, M.: Geometric quantum discord with Bures distance. New J. Phys. 15, 103001 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Spehner, D., Orszag, M.: Geometric quantum discord with Bures distance: the qubit case. J. Phys. A Math. Theor. 47, 035302 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Cerf, N., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using \(d\)-level systems. Phys. Rev. Lett. 88, 127902 (2002)

    ADS  Google Scholar 

  17. Caruso, F., Bechmann-Pasquinucci, H., Macchiavello, C.: Robustness of a quantum key distribution with two and three mutually unbiased bases. Phys. Rev. A. 72, 032340 (2005)

    Article  ADS  Google Scholar 

  18. Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction and orthogonal geometry. Phys. Rev. Lett. 78, 405 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Aharonov, Y., Englert, B.G., Naturforsch, Z.: The mean King’s problem: Spin. A Phys. Sci. 56a, 16 (2001)

  20. Schwinger, J.: Unitary operator bases. Proc. Nat. Acad. Sci. USA, 45 (1960)

  21. Wootters, W.K., Fields, B.D.: Optimal state-determination by mutually unbiased measurements. Ann. Phys. 191, 363 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  22. Bengtsson, I., Bruzda, W., Ericsson, A., Larsson, J.A., Tadej, W., Zyczkowski, K.: Mutually unbiased bases and Hadamard matrices of order six. J. Math. Phys. 48, 052106 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Ivanovic, I.D.: An inequality for the sum of entropies of unbiased quantum measurements. J. Phys. A Math. Gen. 25, 363 (1992)

    Article  ADS  Google Scholar 

  24. Girolami, D.: Observable measure of quantum coherence in finite dimensional systems. Phys. Rev. Lett. 113, 170401 (2014)

    Article  ADS  Google Scholar 

  25. Brierley, S., Weigert, S., Bengtsson, I.: All mutually unbiased bases in dimensions two to five. arXiv:0907.4097v2

  26. Goyal, S.K., Simon, B.N., Singh, R., Simon, S.: Geometry of the generalized Bloch sphere for qutrits. J. Phys. A. Math. Theor. 49, 165203 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Zhang, H.J., Chen, B., Li, M., Fei, S.M., Long, G.L.: Estimation on geometric measure of quantum coherence. Commun. Theor. Phys. 67, (2017)

  28. Rastegin, A.E.: Uncertainty relations for quantum coherence with respect to mutually unbiased bases. Front. Phys. 13, 130304 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by NSFC under Nos 11761073, 11675113 and 12075159, Beijing Municipal Commission of Education (KZ201810028042), Beijing Natural Science Foundation (Grant No. Z190005); Academy for Multidisciplinary Studies, Capital Normal University; Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China (No. SIQSE202001).

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yanbian University, Yanji, 133002, China

    Yi-Hao Sheng, Jian Zhang & Yuan-Hong Tao

  2. Department of Big Data, School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, China

    Yuan-Hong Tao

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei

  4. Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Shao-Ming Fei

Authors
  1. Yi-Hao Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuan-Hong Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shao-Ming Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuan-Hong Tao.

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

Sheng, YH., Zhang, J., Tao, YH. et al. Applications of quantum coherence via skew information under mutually unbiased bases. Quantum Inf Process 20, 82 (2021). https://doi.org/10.1007/s11128-021-03017-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-021-03017-z

Keywords

Search

Navigation