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Monogamy relationship between quantum and classical correlations for continuous variable in curved spacetime

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Abstract

We study the quantum discord, the classical correlation and the monogamy relationship for continuous variable in the background of a Schwarzschild black hole. We find that, as the Hawking temperature increases, the Gaussian discord by measuring the mode A first reduces and then appears freezing phenomenon, while the Gaussian discord by measuring the mode B reduces to zero. The interesting phenomenon is that the classical correlation based on measurement on mode B is not affected by the Hawking radiation and remains constant, while the classical correlation based on measurement on mode A reduces with increasing Hawking temperature. Furthermore, we find two monogamy relationships between quantum and classical correlations, which means that the lost quantum correlation is transformed into the classical correlation by the Hawking effect. This shows that the quantum correlation is not really lost in Schwarzschild black hole, but just converted from one form to another. This has important implications for understanding the black hole information paradox from the perspective of quantum correlation.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 12205133, 1217050862 and 11275064), LJKQZ20222315 and 2021BSL013.

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Authors and Affiliations

  1. Department of Physics, Liaoning Normal University, Dalian, 116029, China

    Shu-Min Wu, Dan-Dan Liu, Chun-Xu Wang, Wen-Mei Li & Xiao-Li Huang

  2. Department of Physics, Hunan Normal University, Changsha, 410081, China

    Hao-Sheng Zeng

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  1. Shu-Min Wu
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  2. Dan-Dan Liu
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  3. Chun-Xu Wang
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  4. Wen-Mei Li
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Correspondence to Xiao-Li Huang or Hao-Sheng Zeng.

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Wu, SM., Liu, DD., Wang, CX. et al. Monogamy relationship between quantum and classical correlations for continuous variable in curved spacetime. Eur. Phys. J. Plus 138, 56 (2023). https://doi.org/10.1140/epjp/s13360-023-03655-5

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