  Quantum state tomography often operates in the highly idealised scenario of
assuming perfect measurements. The errors implied by such an approach are
entwined with other imperfections relating to the information processing
protocol or application of interest. We consider the problem of retrodicting
the quantum state of a system, existing prior to the application of random but
known phase errors, allowing those errors to be separated and removed. The
continuously random nature of the errors implies that there is only one click
per measurement outcome -- a feature having a drastically adverse effect on
data-processing times. We provide a thorough analysis of coarse-graining under
various reconstruction algorithms, finding dramatic increases in speed for only
modest sacrifices in fidelity.
