Monogamy relationship between quantum and classical correlations for continuous variable in curved spacetime
Department of Physics, Liaoning Normal University, 116029, Dalian, China
2 Department of Physics, Hunan Normal University, 410081, Changsha, China
Accepted: 3 January 2023
Published online: 21 January 2023
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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