Continuous measurements play a pivotal role in the study of dynamical open
quantum systems. `Dyne' detections are among the most widespread and efficient
measurement schemes, and give rise to quantum diffusion of the conditioned
state. In this work we study under what conditions the detector dependency of
the conditional state of a quantum system subject to diffusive monitoring can
be demonstrated experimentally, in the sense of ruling our any
detector-independent pure-state dynamical model for the system. We consider an
arbitrary number L of environments to which the system is coupled, and an
arbitrary number K of different types of dyne detections. We prove that
non-trivial necessary conditions for such a demonstration can be determined
efficiently by semi-definite programming. To determine sufficient conditions,
different physical environmental couplings and Hamiltonians for a qubit, and
different sets of diffusive monitorings are scrutinized. We compare the
threshold efficiencies that are sufficient in the various cases, as well as
cases previously considered in the literature, to suggest the most feasible
experimental options.Comment: 11 pages, 5 figures, 1 tabl
