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 entropy production in ideal and in
inefficient monitoring setups. This provides a suitable estimator of
dissipation using imperfect detection records that lower bounds the underlying
entropy production at the level of single trajectories. We illustrate our
findings with a driven-dissipative two-level system following quantum jump
trajectories.Comment: 5 + 10 pages, 2 figures. The two first authors contributed equally to
this wor