  Fluctuation theorems are fundamental results in nonequilibrium thermodynamics
beyond the linear response regime. Among these, the paradigmatic Tasaki-Crooks
fluctuation theorem relates the statistics of the works done in a forward
out-of-equilibrium quantum process and in a corresponding backward one. In
particular, the initial states of the two processes are thermal states and thus
incoherent in the energy basis. Here, we aim to investigate the role of initial
quantum coherence in work fluctuation theorems, by considering a
quasiprobability distribution of work. To do this, we formulate and examine the
implications of a detailed fluctuation theorem, which reproduces the
Tasaki-Crooks fluctuation theorem in the absence of initial quantum coherence.
