  A prime goal of quantum tomography is to provide quantitatively rigorous
characterisation of quantum systems, be they states, processes or measurements,
particularly for the purposes of trouble-shooting and benchmarking experiments
in quantum information science. A range of techniques exist to enable the
calculation of errors, such as Monte-Carlo simulations, but their quantitative
value is arguably fundamentally flawed without an equally rigorous way of
authenticating the quality of a reconstruction to ensure it provides a
reasonable representation of the data, given the known noise sources. A key
motivation for developing such a tool is to enable experimentalists to
rigorously diagnose the presence of technical noise in their tomographic data.
In this work, I explore the performance of the chi-squared goodness-of-fit test
statistic as a measure of reconstruction quality. I show that its behaviour
deviates noticeably from expectations for states lying near the boundaries of
physical state space, severely undermining its usefulness as a quantitative
tool precisely in the region which is of most interest in quantum information
processing tasks. I suggest a simple, heuristic approach to compensate for
these effects and present numerical simulations showing that this approach
provides substantially improved performance.
