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

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

2008-04-14

arxiv.org/abs/0804.2093v2

Annales Henri Poincare 9 (2008), no. 5, 979-1003

Physics

Mathematical Physics

We correct a mistake in the statement of Lemma 1 in the preliminaries section (this has no effect on the proofs and results of

Scientific paper

10.1007/s00023-008-0379-3

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 $\omega$, the net of orthogonal measures representing the net of states $({\mathcal{T}}_{*t}(\omega))$ 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 $\omega$. This implies that $({\mathcal{T}}_{*t}(\omega))$ is faithful for all $t$ large enough. Examples arising in weak coupling limit are studied.

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