  Discrete quantum feedback control consists of a managed dynamics according to
the information acquired by a previous measurement. Energy fluctuations along
such dynamics satisfy generalized fluctuation relations, which are useful tools
to study the thermodynamics of systems far away from equilibrium. Due to the
practical challenge to assess energy fluctuations in the quantum scenario, the
experimental verification of detailed fluctuation relations in the presence of
feedback control remains elusive. We present a feasible method to
experimentally verify detailed fluctuation relations for discrete feedback
control quantum dynamics. Two detailed fluctuation relations are developed and
employed. The method is based on a quantum interferometric strategy that allows
the verification of fluctuation relations in the presence of feedback control.
An analytical example to illustrate the applicability of the method is
discussed. The comprehensive technique introduced here can be experimentally
implemented at a microscale with the current technology in a variety of
experimental platforms.
