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The thermodynamic behavior of Markovian open quantum systems can be describedat 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 anduniversal fluctuation relations are unknown. Here, we fill this gap by derivinga universal fluctuation relation that links thermodynamic entropy productionand information-theoretical irreversibility along single trajectories ininefficient monitoring setups. This relation provides as a corollary anirreversibility estimator of dissipation using imperfect detection records thatlower bounds the underlying entropy production at the level of visibletrajectories. We illustrate our findings with a driven-dissipative two-levelsystem following quantum jump trajectories and discuss the experimentalapplicability of our results for thermodynamic inference.

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