Quasi-free states and a unified treatment of the quantum and thermal fluctuations

Abstract

We show that the pure quasi-free state obtained from a mixed quasi-free state by the purification map is a state with strong quantum correlations between the initial modes and the auxiliary ones. This pure quasi-free state can be obtained from the Fock state by a Bogoliubov automorphism. An inverse map for the purification map is defined. It is shown that this map produces thermal fluctuations from quantum correlations.