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

摘要

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