TU Darmstadt / ULB / TUbiblio

Asymptotic Evolution of Random Unitary Operations

Novotny, Jaroslav ; Alber, Gernot ; Jex, Igor (2010):
Asymptotic Evolution of Random Unitary Operations.
In: Central European Journal of Physics, 8 (6), pp. 1001-1014. DOI: 10.2478/s11534-010-0018-8,
[Article]

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.

Item Type: Article
Erschienen: 2010
Creators: Novotny, Jaroslav ; Alber, Gernot ; Jex, Igor
Title: Asymptotic Evolution of Random Unitary Operations
Language: German
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.

Journal or Publication Title: Central European Journal of Physics
Journal volume: 8
Number: 6
Divisions: 20 Department of Computer Science
Date Deposited: 30 Dec 2016 20:23
DOI: 10.2478/s11534-010-0018-8
Identification Number: TUD-CS-2010-2450
Export:
Suche nach Titel in: TUfind oder in Google
Send an inquiry Send an inquiry

Options (only for editors)
Show editorial Details Show editorial Details