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
Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89(4), 041003 (2017)
Hu, M., Hu, X., Wang, J., et al.: Quantum coherence and geometric quantum discord. Phys. Rep. 762–764, 1–100 (2018)
Dana, K., García, D.łaz M., Mejatty, M., et al.: Resource theory of coherence: beyond states. Phys. Rev. A 95(6), 062327 (2017)
Theurer, T., Killoran, N., Egloff, D., et al.: Resource theory of superposition. Phys. Rev. Lett. 119(23), 230401 (2017)
Liu, Y., Sui, X., Kuang, X., et al.: Object tracking based on vector convolutional network and discriminant correlation filters. Sensors. 19(8), 1818 (2019)
Gour, G., Spekkens, R.: The resource theory of quantum reference frames: manipulations and monotones. New. J. Phys. 10, 033023 (2008)
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)
Xu, J.: Coherence of quantum channels. Phys. Rev. A 100, 052311 (2019)
Liu, Z., Hu, X., Lloyd, S.: Resource destroying maps. Phys. Rev. Lett. 118(6), 060502 (2017)
Chen, Z.: Wigner-Yanase skew information as tests for quantum entanglement. Phys. Rev. A 71(5), 362–366 (2004)
Uhlmann, A.: Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Comm. Math. Phys. 54(1), 21–32 (1977)
Lieb, E.H.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 11(3), 267–288 (1973)
Luo, S.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91(18), 180403 (2003)
Piani, M., Watrous, J.: Necessary and sufficient quantum information characterization of Einstein-Podolsky-Rosen steering. Phys. Rev. Lett. 114(6), 060404 (2015)
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)
Jin, Z., Fei, S.: Quantifying quantum coherence and non-classical correlation based on Hellinger distance. Phys. Rev. A 97(6), 062342 (2018)
Luo, S., Zhang, Q.: Informational distance on quantum-state space. Phys. Rev. A 69(3), 183–186 (2004)
Luo, S.: Wigner-Yanase skew information versus quantum Fisher information. P. Am. Math. Soc. 132(3), 885–890 (2004)
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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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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DOI: https://doi.org/10.1007/s11128-022-03802-4