We demonstrate a method for finding the decoherence-subalgebra $\mathcal{ N}(\mathcal{ T})$ of a Gaussian quantum Markov semigroup on the von Neumann algebra $\mathcal{ B}(\Gamma(\mathbb{ C}^d))$ of all bounded operator on the Fock space $\Gamma(\mathbb{ C}^d)$ on $\mathbb{ C}^d$. We show that $\mathcal{ N}(\mathcal{ T})$ is a type I von Neumann algebra $L^\infty(\mathbb{ R}^{ d_c};\mathbb{ C})\bar{ \otimes}\mathcal{ B}(\Gamma(\mathbb{ C}^{ d_f}))$ determined, up to unitary equivalence, by two natural numbers $d_c,d_f\leq d$. This result is illustrated by some applications and examples.
Categories: quant-ph