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Measurement-induced entropy increment for quantifying genuine coherence

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Abstract

Coherence is an important quantum resource in quantum information theory and can be quantified by entropy. We propose a class of genuine coherence quantity which is defined via the difference of entropies between the state \(\varrho \) and the dephased state \(\Delta [\varrho ]\). One can employ Tsallis-\(\alpha \) entropy and Rényi-\(\alpha \) entropy for this genuine coherence quantity and regard it as the measurement-induced entropy increment, since it can be related to the optimal average work in quantum thermodynamics with thermodynamics project measurements. We prove that the quantity is genuine coherence monotone but not genuine coherence measure. Furthermore, we present an improved coherence quantity, which can be proved as a coherence measure.

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Acknowledgements

We thank S. Camalet, Ming-Liang Hu, Xueyuan Hu for helpful discussions. This work is supported by the National Natural Science Foundation of China (Grants No. 11734015 and No. 61674110), and K.C. Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. School of Physical Science and Technology, Soochow University, Suzhou, 215006, China

    Yue Dai, Jun Hu, Zhou Zhang, Yuli Dong & Xuefeng Wang

  2. School of Physical Science and Technology, Ningbo University, Ningbo, 315211, China

    Chengjie Zhang

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  1. Yue Dai
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Correspondence to Chengjie Zhang.

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Dai, Y., Hu, J., Zhang, Z. et al. Measurement-induced entropy increment for quantifying genuine coherence. Quantum Inf Process 20, 261 (2021). https://doi.org/10.1007/s11128-021-03199-6

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