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arXiv · 0804.2093

Large deviations for quantum Markov semigroups on the 2 x 2 matrix algebra

Henri Comman
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Abstract

Let $({\mathcal{T}}_{*t})$ be a predual quantum Markov semigroup acting on the full 2 x 2 matrix algebra and having an absorbing pure state. We prove that for any initial state $ω$, the net of orthogonal measures representing the net of states $({\mathcal{T}}_{*t}(ω))$ satisfies a large deviation principle in the pure state space, with a rate function given in terms of the generator, and which does not depend on $ω$. This implies that $({\mathcal{T}}_{*t}(ω))$ is faithful for all $t$ large enough. Examples arising in weak coupling limit are studied.

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Henri Comman. 2008-10-06. Large deviations for quantum Markov semigroups on the 2 x 2 matrix algebra. https://doi.org/10.1007/s00023-008-0379-3

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