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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 5, 2010

Asymptotic evolution of random unitary operations

  • Jaroslav Novotný EMAIL logo , Gernot Alber and Igor Jex
From the journal Open Physics

Abstract

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.

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Published Online: 2010-9-5
Published in Print: 2010-12-1

© 2010 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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