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Quantum \(\alpha \)-fidelity of unitary orbits

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Abstract

The extremum values of quantum \(\alpha \)-fidelity under unitary orbits of quantum states are explicitly derived by applying rearrangement inequalities, matrix trace inequalities, and theory of majorization. Furthermore, the \(\alpha \)-fidelity is successfully verified to go through the whole closed interval, which works from the minimum value to the maximum value.

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Acknowledgements

We thank the anonymous referees for their useful comments. We also would like to thank professor Zhongjin Ruan, professor Marius Junge, Lin Zhang, Haojian Li, Yao Li for very helpful discussions and comments. This work is supported by National Natural Science Foundation of China (Grants Nos. 11771106 and 61871156).

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Authors and Affiliations

  1. School of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Xiaojing Yan & Longsuo Li

  2. Institute of Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, 150006, People’s Republic of China

    Zhi Yin

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  1. Xiaojing Yan
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  2. Zhi Yin
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  3. Longsuo Li
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Correspondence to Longsuo Li.

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Yan, X., Yin, Z. & Li, L. Quantum \(\alpha \)-fidelity of unitary orbits. Quantum Inf Process 19, 307 (2020). https://doi.org/10.1007/s11128-020-02805-3

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