Quantum Large Deviations

Abstract: We reconsider the quantum analogue of Varadhans Theorem proved by Petz, Raggio and Verbeure. They proved this theorem using standard techniques in quantum statistical mechanics of lattice systems to arrive at a variational formula over states on an operator algebra, which can subsequently be reduced to a variational formula in terms of a single real variable. In this paper a new proof is given using a quantum version of the large deviation analysis together with the Trotter product formula. The proof is subsequently extended to the general case of q non-commuting variables resulting in a variational formula for general mean-field quantum spin systems as first derived by Raggio and Werner.