Steady state coherence in a qubit is incompatible with a quantum map

TL;DR

The paper demonstrates that steady state coherence in a qubit cannot be maintained within a proper quantum map framework, highlighting limitations of certain approaches in describing open quantum systems.

Contribution

It shows that steady state coherence in a qubit is incompatible with quantum maps by analyzing different theoretical descriptions and their physical consistency.

Findings

Redfield approach yields steady state coherences but violates quantum map properties.

Lindblad equation enforces proper quantum map but predicts no steady state coherence.

Steady state coherence in a qubit is fundamentally incompatible with quantum maps.

Abstract

We consider the recent proposal of steady state coherences in a single qubit in the case of a composite system-bath interaction. Based on a field theoretical approach we reanalyse the issue within a Redfield description. We find that the Redfield approach in accordance with a recent proposal yields steady state coherences but also violates the properties of a quantum map yielding negative populations. The issue is resolved by applying the Lindblad equation which is in accordance with a proper quantum map. The Lindblad equation, however, also implies the absence of steady state coherence. We conclude that steady state coherence in a a qubit is incompatible with a quantum map.