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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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Volume 8, Issue 6


Volume 13 (2015)

Asymptotic evolution of random unitary operations

Jaroslav Novotný
  • Institut für Angewandte Physik, Technische Universität Darmstadt, Hochschulstraße 4a, D-64289, Darmstadt, Germany
  • Department of Physics, FJFI ČVUT v Praze, Břehová 7 Praha 1 - Staré Město, 115 19, Prague, Czech Republic
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Gernot Alber
  • Institut für Angewandte Physik, Technische Universität Darmstadt, Hochschulstraße 4a, D-64289, Darmstadt, Germany
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/ Igor Jex
Published Online: 2010-09-05 | DOI: https://doi.org/10.2478/s11534-010-0018-8


We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.

Keywords: random unitary map; asymptotic evolution; iterations; attractor; open dynamics

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About the article

Published Online: 2010-09-05

Published in Print: 2010-12-01

Citation Information: Open Physics, Volume 8, Issue 6, Pages 1001–1014, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-010-0018-8.

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© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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