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Entropy production of quantum Markov semigroup associated with open quantum walks on the periodic graphs

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Abstract

In this paper, we compute the entropy production of quantum Markov semigroup associated with open quantum walks. The entropy production, for the classical as well as quantum systems, measures the deviation from the symmetry between the forward and backward processes. The detailed balance condition with respect to an invariant state is the condition for the symmetry of the dynamics. Here we consider the quantum Markov semigroups associated with open quantum walks on the periodic graphs. On the one hand, the model serves as a good example to study the quantum detailed balance condition and the entropy production. On the other hand, from the viewpoint of the dynamics itself, the concept of entropy production helps for a better understanding of the dynamics.

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Acknowledgements

We are grateful to the anonymous referee for valuable comments on the first version of the manuscript. The work of HJY was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean government (MSIT) (No. 2020R1F1A101075).

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The authors have no relevant financial or non-financial interests to disclose.

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Authors and Affiliations

  1. University College, Yonsei University, 85 Songdogwahak-ro, Yeonsu-gu, Incheon, 21983, Korea

    Chul Ki Ko

  2. School of Computer Engineering and Applied Mathematics, and Institute for Integrated Mathematical Sciences, Hankyong National University, 327 Jungang-ro, Anseong-si, Gyeonggi-do, 17579, Korea

    Hyun Jae Yoo

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  1. Chul Ki Ko
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  2. Hyun Jae Yoo
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Correspondence to Hyun Jae Yoo.

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Ko, C.K., Yoo, H.J. Entropy production of quantum Markov semigroup associated with open quantum walks on the periodic graphs. Quantum Inf Process 22, 81 (2023). https://doi.org/10.1007/s11128-023-03827-3

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