Fluctuation theorems are one of the pillars of nonequilibrium thermodynamics. Broadly speaking, they concern the statistical distribution of quantities such as heat, work, or entropy production. Quantum experiments, however, usually can only assess these distributions indirectly, or reconstruct them a posteriori. In this Letter we report an experiment where the distribution of entropy production is obtained directly from the outcomes (clicks) of an optical experiment simulating the interaction between a two-level system and a thermal reservoir. The setup consists of entangled photon pairs, one of which is sent to an interferometer implementing a finite-temperature amplitude damping channel, and is designed so as to allow full access to the two-point measurement statistics of both system and reservoir. First, by measuring the entangled pair, we directly implement the two-point measurement scheme in the system, avoiding the destructive nature of photodetection. Second, each optical path of the interferometer is associated with a specific transition of the reservoir. Thus, by blocking all but one of the paths, we can measure the conditional entropy production, given a specific reservoir trajectory.

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• Open quantum systems & decoherence
• Quantum measurements
• Quantum optics
• Quantum thermodynamics