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Abstract: We analyze the asymptotic dynamics of quantum systems resulting from largenumbers of iterations of random unitary operations. Although, in general, thesequantum operations cannot be diagonalized it is shown that their resultingasymptotic dynamics is described by a diagonalizable superoperator. We provethat this asymptotic dynamics takes place in a typically low dimensionalattractor space which is independent of the probability distribution of theunitary operations applied. This vector space is spanned by all eigenvectors ofthe unitary operations involved which are associated with eigenvalues of unitmodulus. Implications for possible asymptotic dynamics of iterated randomunitary operations are presented and exemplified in an example involving randomcontrolled-not operations acting on two qubits.

Author: J. Novotny, G. Alber, I. Jex


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