  We develop a martingale theory to describe fluctuations of entropy production
for open quantum systems in nonequilbrium steady states. Using the formalism of
quantum jump trajectories, we identify a decomposition of entropy production
into an exponential martingale and a purely quantum term, both obeying integral
fluctuation theorems. An important consequence of this approach is the
derivation of a set of genuine universal results for stopping-time and infimum
statistics of stochastic entropy production. Finally we complement the general
formalism with numerical simulations of a qubit system.
