Journal
PHYSICS LETTERS A
Volume 373, Issue 3, Pages 320-324Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2008.11.043
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Funding
- SFB Transregio-12 project
- European grant COCOS
- Polish Ministry of Science and Education [N202 099 31/0746]
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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. (C) 2008 Elsevier B.V. All rights reserved.
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