Asymptotic evolution of random unitary operations

• Authors: Jaroslav Novotný , Gernot Alber , Igor Jex
• Languages of publication: EN

Abstracts

EN

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

EN

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

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2010
• Volume: 8
• Issue: 6
• Pages: 1001-1014

Dates

published

1 - 12 - 2010

online

5 - 9 - 2010

Contributors

author

Jaroslav Novotný

author

Gernot Alber

• Institut für Angewandte Physik, Technische Universität Darmstadt, Hochschulstraße 4a, D-64289, Darmstadt, Germany

author

Igor Jex

• Department of Physics, FJFI ČVUT v Praze, Břehová 7 Praha 1 - Staré Město, 115 19, Prague, Czech Republic

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Identifiers

DOI

10.2478/s11534-010-0018-8