The Decoherence-Free Subalgebra of Gaussian Quantum Markov Semigroups

Agredo, Julián | 2022-06-03

We demonstrate a method for finding the decoherence-free subalgebra N(T) of a Gaussian quantum Markov semigroup on the von Neumann algebra B(Γ(Cd)) of all bounded operator on the Fock space Γ(Cd) on Cd . We show that N(T) is a type I von Neumann algebra L∞(Rdc;C)⊗¯¯¯¯B(Γ(Cdf)) determined, up to unitary equivalence, by two natural numbers dc,df≤d . This result is illustrated by some applications and examples.