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Quantum coherence via skew information for quantum channels

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Abstract

Recently, various resource theories of physical properties are extensively studied. In particular, the resource theory of quantum coherence with respect to a quantum channel is also investigated. In this paper, instead of quantifying coherence existing in a state, we present a quantifier of coherence for a quantum channel via skew information. We then show that the coherence quantifier fits the framework of quantifying coherence of a quantum channel. As an application of our result, we show that the superiority of a quantum channel in sub-superchannel discrimination can be precisely characterized by the coherence via skew information of a quantum channel. A similar notion induced by Hellinger distance can also be established for a quantum channel, which we called the Hellinger distance coherence of a quantum channel. Moreover, we show that there is a quantitative relationship between the coherence via skew information of a quantum channel and the Hellinger distance coherence measure of this quantum channel.

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References

  1. Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89(4), 041003 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  2. Hu, M., Hu, X., Wang, J., et al.: Quantum coherence and geometric quantum discord. Phys. Rep. 762–764, 1–100 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  3. Dana, K., García, D.łaz M., Mejatty, M., et al.: Resource theory of coherence: beyond states. Phys. Rev. A 95(6), 062327 (2017)

    Article  ADS  Google Scholar 

  4. Theurer, T., Killoran, N., Egloff, D., et al.: Resource theory of superposition. Phys. Rev. Lett. 119(23), 230401 (2017)

    Article  ADS  Google Scholar 

  5. Liu, Y., Sui, X., Kuang, X., et al.: Object tracking based on vector convolutional network and discriminant correlation filters. Sensors. 19(8), 1818 (2019)

    Article  ADS  Google Scholar 

  6. Gour, G., Spekkens, R.: The resource theory of quantum reference frames: manipulations and monotones. New. J. Phys. 10, 033023 (2008)

    Article  ADS  Google Scholar 

  7. Carlini, A., Sasaki, M.: Geometrical conditions for completely positive trace-preserving maps and their application to a quantum repeater and a state-dependent quantum cloning machine. Phys. Rev. A 4, 68 (2003)

    Google Scholar 

  8. Xu, J.: Coherence of quantum channels. Phys. Rev. A 100, 052311 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  9. Liu, Z., Hu, X., Lloyd, S.: Resource destroying maps. Phys. Rev. Lett. 118(6), 060502 (2017)

    Article  ADS  Google Scholar 

  10. Chen, Z.: Wigner-Yanase skew information as tests for quantum entanglement. Phys. Rev. A 71(5), 362–366 (2004)

    Google Scholar 

  11. Uhlmann, A.: Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Comm. Math. Phys. 54(1), 21–32 (1977)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Lieb, E.H.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 11(3), 267–288 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  13. Luo, S.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91(18), 180403 (2003)

    Article  ADS  Google Scholar 

  14. Piani, M., Watrous, J.: Necessary and sufficient quantum information characterization of Einstein-Podolsky-Rosen steering. Phys. Rev. Lett. 114(6), 060404 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  15. Jin, Z., Yang, L., Fei, S., et al.: Maximum relative entropy of coherence for quantum channels. Sci. China. Phys. Mech. 64(8), 1–6 (2021)

    Article  Google Scholar 

  16. Jin, Z., Fei, S.: Quantifying quantum coherence and non-classical correlation based on Hellinger distance. Phys. Rev. A 97(6), 062342 (2018)

    Article  ADS  Google Scholar 

  17. Luo, S., Zhang, Q.: Informational distance on quantum-state space. Phys. Rev. A 69(3), 183–186 (2004)

    Article  MathSciNet  Google Scholar 

  18. Luo, S.: Wigner-Yanase skew information versus quantum Fisher information. P. Am. Math. Soc. 132(3), 885–890 (2004)

    Article  MATH  Google Scholar 

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Acknowledgements

This work is supported by the NSF of China under Grant No. 11961073. We are grateful to Nan Li and Lin Zhang for improving the equality of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yanbian University, Yanji, 133002, People’s Republic of China

    Dongping Xuan, Xiaohui Hu & Hua Nan

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  1. Dongping Xuan
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  2. Xiaohui Hu
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  3. Hua Nan
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Correspondence to Hua Nan.

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Xuan, D., Hu, X. & Nan, H. Quantum coherence via skew information for quantum channels. Quantum Inf Process 22, 48 (2023). https://doi.org/10.1007/s11128-022-03802-4

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