Large Deviations for Quantum Markov Semigroups on the 2 × 2-Matrix Algebra

摘要

Let $({mathcal{T}}_{*t})$ be a predual quantum Markov semigroup acting on the full 2 × 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 $({mathcal{T}}_{*t}(omega))$ 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 ω. This implies that $({mathcal{T}}_{*t}(omega))$ is faithful for all t large enough. Examples arising in weak coupling limit are studied.