The Decoherence-Free Subalgebra of Gaussian Quantum Markov Semigroups

Abstract

We demonstrate a method for finding the decoherence-free subalgebra $\mathcal{N(T)}$ 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 is a type I von Neumann algebra $L^{\infty}(\mathbb{R}^{d_c},\mathbb{C})\overline\otimes\mathcal{B}(\Gamma(\mathbb{C}^d))$ determined, up to unitary equivalence, by two natural numbers $d_c,d_f\leq d$. This result is illustrated by some applications and examples.

Julián Andrés Agredo Echeverry

Associate Professor