English

Random Quantum Operations

Exactly Solvable and Integrable Systems 2009-02-24 v2 Quantum Physics

Abstract

We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Phi associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Phi and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.

Keywords

Cite

@article{arxiv.0804.2361,
  title  = {Random Quantum Operations},
  author = {Wojciech Bruzda and Valerio Cappellini and Hans-Jürgen Sommers and Karol Życzkowski},
  journal= {arXiv preprint arXiv:0804.2361},
  year   = {2009}
}
R2 v1 2026-06-21T10:31:01.521Z