Markov property of Gaussian states of canonical commutation relation algebras

The Markov property of Gaussian states of canonical commutation relation algebras is studied. The detailed description is given by the representing block matrix. The proof is short and allows infinite dimension. The relation to classical Gaussian Markov triplets is also described. The minimizer of relative entropy with respect to a Gaussian Markov state has the Markov property. The appendix contains formulas for the relative entropy. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3253974]