On the existence of the KMS spectral gap in Gaussian quantum Markov semigroups

TL;DR

This paper establishes a necessary and sufficient condition for the existence of the KMS spectral gap in Gaussian quantum Markov semigroups, linking it to the noise operators and the GNS spectral gap.

Contribution

It provides a new criterion for the KMS spectral gap based solely on the noise operators, extending previous results on the GNS spectral gap.

Findings

The KMS spectral gap exists if and only if certain conditions on noise operators are met.

Existence of the GNS spectral gap implies the KMS spectral gap.

The paper characterizes spectral gaps in Gaussian quantum Markov semigroups.

Abstract

In arXiv:2405.04947, it was shown that the GNS spectral gap of a Gaussian quantum Markovian generator is strictly positive if and only if there exists a maximal number of linearly independent noise operators, under the assumption that the generated semigroup admits a unique faithful normal invariant state. In this paper, we provide a necessary and sufficient condition for the existence of the KMS spectral gap, which also depends only on the noise operators of the generator. We further show that the existence of the GNS spectral gap implies the existence of the KMS spectral gap.