Composition of quantum operations and products of random matrices

Details Composition of quantum operations and products of random matrices Composition of quantum operations and products of random matrices

2011-05-19

arxiv.org/abs/1105.3830v1

Acta Physica Polonica B, Vol. 42, 1123 (2011)

Physics

Quantum Physics

19 pages, 7 figures

Scientific paper

Spectral properties of evolution operators corresponding to random maps and quantized chaotic systems strongly interacting with an environment can be described by the ensemble of non-hermitian random matrices from the real Ginibre ensemble. We analyze evolution operators Psi=Psi_s...Psi_1 representing the composition of s random maps and demonstrate that their complex eigenvalues are asymptotically described by the law of Burda et al. obtained for a product of s independent random complex Ginibre matrices. Numerical data support the conjecture that the same results are applicable to characterize the distribution of eigenvalues of the s-th power of a random Ginibre matrix. Squared singular values of Psi are shown to be described by the Fuss-Catalan distribution of order s. Results obtained for products of random Ginibre matrices are also capable to describe the s-step evolution operator for a model deterministic dynamical system - a generalized quantum baker map subjected to strong interaction with an environment.

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