Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-04-15
Phys. Lett. A 373, 320-324 (2009).
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
10.1016/j.physleta.2008.11.043
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.
Bruzda Wojciech
Cappellini Valerio
Sommers Hans--J{ü}rgen
Zyczkowski Karol
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