The general structure of the Decoherence-free subalgebra for uniformly continuous Quantum Markov semigroups

TL;DR

This paper provides a structural theorem for the decoherence-free subalgebra of uniformly continuous quantum Markov semigroups, showing it is atomic when a faithful invariant state exists, indicating decoherence occurs.

Contribution

It introduces a decomposition-based structure theorem for decoherence-free subalgebras in uniformly continuous QMSs, highlighting conditions for atomicity and decoherence.

Findings

N(T) can be decomposed into direct integrals of factors.

When a faithful normal invariant state exists, N(T) is atomic.

Decoherence occurs when N(T) is atomic.

Abstract

By using the decomposition of the decoherence-free subalgebra N(T) in direct integrals of factors, we obtain a structure theorem for every uniformly continuous QMSs. Moreover we prove that, when there exists a faithful normal invariant state, N(T) has to be atomic and decoherence takes place.