Composition of quantum operations and products of random matrices

Wojciech Roga, Marek Smaczynski, Karol Życzkowski

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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 Ψ = Ψs…Ψ1 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 Ψ are shown to be described by the Fuss–Catalan distribution of the order of 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.
Original languageEnglish
Pages (from-to)1123-1140
Number of pages18
JournalActa Physica Polonica B
Volume42
Issue number5
DOIs
Publication statusPublished - 31 May 2011

Keywords

  • complex eigenvalues
  • quantum operators
  • random matrices
  • matrix
  • deterministic dynamical systems
  • quantum baker map

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