Abstract
We consider a situation when evolution of an entangled Einstein–Podolsky–Rosen (EPR) pair takes place in a regime of quantum chaos being chaotic in the classical limit. This situation is studied on an example of chaotic pair dynamics described by the quantum Chirikov standard map. The time evolution is reversible even if a presence of small errors breaks time reversal of classical dynamics due to exponential growth of errors induced by exponential chaos instability. However, the quantum evolution remains reversible since a quantum dynamics instability exists only on a logarithmically short Ehrenfest time scale. We show that due to EPR pair entanglement a measurement of one particle at the moment of time reversal breaks exact time reversal of another particle which demonstrates only an approximat time reversibility. This result is interpreted in the framework of the Schmidt decomposition and Feynman path integral formulation of quantum mechanics. The time reversal in this system has already been realized with cold atoms in kicked optical lattices in absence of entanglement and measurements. On the basis of the obtained results, we argue that the experimental investigations of time reversal of chaotic EPR pairs are within reach of present cold atom capabilities.
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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All results and data are presented in this manuscript and Supporting Material.]
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31 October 2021
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Acknowledgements
This research was supported in part through the grant NANOX \(N^o\) ANR-17-EURE-0009, (project MTDINA) in the frame of the Programme des Investissements d’Avenir, France; the work is also done as a part of the ANR France project OCTAVES. This work was granted access to the HPC resources of CALMIP (Toulouse) under the allocation 2021-P0110.
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Frahm, K.M., Shepelyansky, D.L. Chaotic Einstein–Podolsky–Rosen pairs, measurements and time reversal. Eur. Phys. J. D 75, 277 (2021). https://doi.org/10.1140/epjd/s10053-021-00274-6
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DOI: https://doi.org/10.1140/epjd/s10053-021-00274-6