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Asymmetry of Locally Available and Locally Transmitted Information in Thermal Two-Qubit States

Journal of Mathematical Sciences volume 252, pages 43–59 (2021)Cite this article

Abstract

In the paper, we consider thermal states of two particles with spin 1/2 (qubits) located in an inhomogeneous transverse magnetic field and interacting according to the Heisenberg XY -model. We introduce the concepts of magnitude and direction of asymmetry of the entropy of a state and the magnitude and asymmetry of a flow of locally transmitted information. We show that for the system considered, the asymmetry of entropy is directed from the particle in a weaker magnetic field toward the particle in a stronger magnetic field, and this direction coincides with the direction of the excess flow of locally transmitted information. We also demonstrate that this asymmetry direction is consistent with the direction of the excess flow of locally available information: measurements over the particle in a weaker magnetic field provide a greater level of locally available information than measurements over the particle in a stronger magnetic field.

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Authors and Affiliations

  1. V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, Moscow, Russia

    E. O. Kiktenko

  2. Russian Quantum Center, Skolkovo, Moscow, Russia

    E. O. Kiktenko

  3. Bauman Moscow State Technical University, Moscow, Russia

    E. O. Kiktenko

  4. Geoelectromagnetic Research Center of the Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences, Troitsk, Moscow, Russia

    E. O. Kiktenko

Authors
  1. E. O. Kiktenko
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Correspondence to E. O. Kiktenko.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 151, Quantum Probability, 2018.

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Cite this article

Kiktenko, E.O. Asymmetry of Locally Available and Locally Transmitted Information in Thermal Two-Qubit States. J Math Sci 252, 43–59 (2021). https://doi.org/10.1007/s10958-020-05140-1

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  • DOI: https://doi.org/10.1007/s10958-020-05140-1

Keywords and phrases

  • quantum discord
  • Heisenberg XY -interaction
  • locally available information

AMS Subject Classification

  • 81V99
  • 81Q99