The Decoherence-Free Subalgebra of Gaussian Quantum Markov Semigroups

We demonstrate a method for finding the decoherence-free subalgebra N(T) of a Gaussian quantum Markov semigroup on the von Neumann algebra B(Gamma(C-d)) of all bounded operator on the Fock space Gamma(C-d) on C-d. We show that N(T) is a type I von Neumann algebra L-infinity (R-dc;C)(circle times) over barB(Gamma(C-df)) determined, up to unitary equivalence, by two natural numbers d(c), d(f) <= d. This result is illustrated by some applications and examples.