The decoherence-free subalgebra of Gaussian Quantum Markov Semigroups

Abstract

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 $d_c,d_f\le d$. This result is illustrated by some applications and examples.

References in corpus (2)

• Irreversible quantum evolution with quadratic generator: Review
• Symmetry and block structure of the Liouvillian superoperator in partial secular approximation