  Elucidating the energy transfer between a quantum system and a reservoir is a
central issue in quantum non-equilibrium thermodynamics, which could provide
novel tools to engineer quantum-enhanced heat engines. The lack of information
on the reservoir inherently limits the practical insight that can be gained on
the exchange process of open quantum systems. Here, we investigate the energy
transfer for an open quantum system in the framework of quantum fluctuation
relations. As a novel toolbox, we employ a nitrogen-vacancy center spin qubit
in diamond, subject to repeated quantum projective measurements and a tunable
dissipation channel. In the presence of energy fluctuations originated by
dissipation and quantum projective measurements, the experimental results,
supplemented by numerical simulations, show the validity of the energy exchange
fluctuation relation, where the energy scale factor encodes missing reservoir
information in the system out-of-equilibrium steady state properties. This
result is complemented by a theoretical argument showing that, also for an open
three-level quantum system, the existence of an out-of-equilibrium steady state
dictates a unique time-independent value of the energy scale factor for which
the fluctuation relation is verified. Our findings pave the way to the
investigation of energy exchange mechanisms in arbitrary open quantum systems.
