Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection

TL;DR

This paper derives a universal fluctuation relation connecting entropy production and irreversibility in monitored quantum systems with imperfect detection, enabling thermodynamic inference from incomplete measurement data.

Contribution

It introduces a universal fluctuation relation for entropy production under imperfect detection in monitored quantum systems, filling a key gap in quantum thermodynamics.

Findings

Derived a fluctuation relation linking entropy production and irreversibility.

Provided an irreversibility estimator that bounds entropy production from imperfect data.

Illustrated results with a driven two-level quantum system.

Abstract

The thermodynamic behavior of Markovian open quantum systems can be described at the level of fluctuations by using continuous monitoring approaches. However, practical applications require assessing imperfect detection schemes, where the definition of main thermodynamic quantities becomes subtle and universal fluctuation relations are unknown. Here, we fill this gap by deriving a universal fluctuation relation that links thermodynamic entropy production and information-theoretical irreversibility along single trajectories in inefficient monitoring setups. This relation provides as a corollary an irreversibility estimator of dissipation using imperfect detection records that lower bounds the underlying entropy production at the level of visible trajectories. We illustrate our findings with a driven-dissipative two-level system following quantum jump trajectories and discuss the experimental applicability of our results for thermodynamic inference.