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Fluctuation theorems and the second law of thermodynamics are powerfulrelations constraining the behavior of out-of-equilibrium systems. While thereexist generalizations of these relations to feedback controlled quantumsystems, their applicability is limited, in particular when considering strongand continuous measurements. In this letter, we overcome this shortcoming byderiving a novel fluctuation theorem, and the associated second law ofinformation thermodynamics, which remain applicable in arbitrary feedbackcontrol scenarios. In our second law, the entropy production is bounded by thecoarse-grained entropy production which is inferrable from the measurementoutcomes, an experimentally accessible quantity that does not diverge evenunder strong continuous measurements. We illustrate our results by a qubitundergoing discrete and continuous measurement, where our approach provides auseful bound on the entropy production for all measurement strengths.

Quantum Fluctuation Theorem for Arbitrary Measurement and Feedback Schemes