Markov triplets on CCR-algebras

Abstract

The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is defined by constant entropy increase. The Markov property of a quasi-free state is described by the representing block matrix. The proof is based on results on the statistical sufficiency in the quantum case. The relation to classical Gaussian Markov triplets is also described.