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arXiv · 0804.2361

Random Quantum Operations

Wojciech Bruzda·Valerio Cappellini·Hans-Jürgen Sommers·Karol Życzkowski
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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.

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Wojciech Bruzda, Valerio Cappellini, Hans-Jürgen Sommers, Karol Życzkowski. 2008-10-15. Random Quantum Operations. https://doi.org/10.1016/j.physleta.2008.11.043

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