  The Gorini-Kossakowski-Sudarshan-Lindblad master equation (ME) governs the
density matrix of open quantum systems (OQSs). When an OQS is subjected to weak
continuous measurement, its state evolves as a stochastic quantum trajectory,
whose statistical average solves the ME. The ensemble of such trajectories is
termed an unraveling of the ME. We propose a method to operationally
distinguish unravelings produced by the same ME in different measurement
scenarios, using nonlinear averages of observables over trajectories. We apply
the method to the paradigmatic quantum nonlinear system of resonance
fluorescence in a two-level atom. We compare the Poisson-type unraveling,
induced by direct detection of photons scattered from the two-level emitter,
and the Wiener-type unraveling, induced by phase-sensitive detection of the
emitted field. We show that a quantum-trajectory-averaged variance is able to
distinguish these measurement scenarios. We evaluate the performance of the
method, which can be readily extended to more complex OQSs, under a range of
realistic experimental conditions.
