Relationships between the decoherence-free algebra and the set of fixed points

TL;DR

This paper explores the connection between decoherence-free algebras and fixed points in quantum Markov semigroups, providing characterizations and equivalences relevant for quantum decoherence understanding.

Contribution

It establishes the equivalence between atomicity of decoherence-free subalgebras and environmental decoherence, and characterizes reversible states in this context.

Findings

Atomicity of decoherence-free algebra is equivalent to environmental decoherence.

Explicit description of the relationship between decoherence-free and fixed point subalgebras.

Characterization of reversible states in quantum Markov semigroups.

Abstract

We show that, for a Quantum Markov Semigroup (QMS) with a faithful normal invariant state, the atomicity of the decoherence-free subalgebra and environmental decoherence are equivalent. Moreover, we characterize the set of reversible states and explicitly describe the relationship between the decoherence-free subalgebra and the fixed point subalgebra for QMSs with the above equivalent properties.