The Decoherence-Free Subalgebra of Gaussian Quantum Markov Semigroups

Abstract

We demonstrate a method for finding the decoherence-free 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}){overline{otimes }}{mathcal {B}}(Gamma (mathbb {C}^{d_f})) determined, up to unitary equivalence, by two natural numbers d_c,d_fle d. This result is illustrated by some applications and examples.