  Fluctuation theorems are one of the pillars of non-equilibrium
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. In this letter
we provide an experimental demonstration of a quantum fluctuation theorem where
the distribution of entropy production is obtained directly from the outcomes
(clicks) of an optical experiment. The setup consists of entangled photon
pairs, one of which is sent an interferometer emulating a finite temperature
amplitude damping device. Blocking specific paths of the interferometer is
tantamount to restricting the possible configurations of the reservoir. And by
measuring its entangled pair, we can directly implement the two-point
measurement scheme, thus avoiding the destructive nature of photo-detection.
