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 quasifree state is described by the representing block matrix. The proof is based on results on the statistical sufficiency in the non-commutative case. The relation to classical Gaussian Markov triplets is also described.
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