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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 151, Pages 45–61 (Mi into339)

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

E. O. Kiktenkoabcd

a Steklov Mathematical Institute of Russian Academy of Sciences
b International Center for Quantum Optics and Quantum Technologies (Russian Quantum Center), Moscow, Skolkovo
c Bauman Moscow State Technical University
d Geoelectromagnetic Research Institute, Russian Academy of Scienses

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 the 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 flux 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.

Keywords: quantum discord, $XY$-Heisenberg interaction, locally available information

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÌÊ-2815.2017.1 This work was supported by the Grant of the President of the Russian Federation MK-2815.2017.1.

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English version:
Journal of Mathematical Sciences (New York), 2021, 252:1, 43–59

Bibliographic databases:

UDC: 530.145.1
MSC: 81V99, 81Q99

Citation: E. O. Kiktenko, “Asymmetry of Locally Available and Locally Transmitted Information in Thermal Two-Qubit States”, Quantum probability, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 151, VINITI, Moscow, 2018, 45–61; J. Math. Sci. (N. Y.), 252:1 (2021), 43–59

Citation in format AMSBIB
\Bibitem{Kik18} \by E.~O.~Kiktenko \paper Asymmetry of Locally Available and Locally Transmitted Information in Thermal Two-Qubit States \inbook Quantum probability \serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. \yr 2018 \vol 151 \pages 45--61 \publ VINITI \publaddr Moscow \mathnet{http://mi.mathnet.ru/into339} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3903365} \zmath{https://zbmath.org/?q=an:07282999} \transl \jour J. Math. Sci. (N. Y.) \yr 2021 \vol 252 \issue 1 \pages 43--59 \crossref{https://doi.org/10.1007/s10958-020-05140-1} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85096370495}