  In this article, we revisit the century-old question of the minimal set of
observables needed to identify a quantum state: here, we replace the natural
coincidences in their spectra by effective ones, induced by an imperfect
measurement. We show that if the detection error is smaller than the mean level
spacing, then two observables with Poisson spectra will suffice, no matter how
large the system is. The primary target of our findings is the integrable (i.e.
exactly solvable) quantum systems whose spectra do obey the Poisson statistics.
We also consider the implications of our findings for classical pattern
recognition techniques.
