  We investigate the capabilities of loss-tolerant quantum state
characterization using a photon-number resolving, time-multiplexed detector
(TMD). We employ the idea of probing the Wigner function point-by-point in
phase space via photon parity measurements and displacement operations,
replacing the conventional homodyne tomography. Our emphasis lies on
reconstructing the Wigner function of non-Gaussian Fock states with highly
negative values in a scheme that is based on a realistic experimental setup. In
order to establish the concept of loss-tolerance for state characterization we
show how losses can be decoupled from the impact of other experimental
imperfections, i.e. the non-unity transmittance of the displacement
beamsplitter and non-ideal mode overlap. We relate the experimentally
accessible parameters to effective ones that are needed for an optimised state
reconstruction. The feasibility of our approach is tested by Monte Carlo
simulations, which provide bounds resulting from statistical errors that are
due to limited data sets. Our results clearly show that high losses can be
accepted for a defined parameter range, and moreover, that (in contrast to
homodyne detection) mode mismatch results in a distinct signature, which can be
evaluated by analysing the photon number oscillations of the displaced Fock
states.
