  Photon-number resolving detectors are a fundamental building-block of optical
quantum information processing protocols. A loop detector, combined with
appropriate statistical processing, can be used to convert a binary on/off
photon counter into a photon-number-resolving detector. Here we describe the
idea of a signature of photon-counts, which may be used to more robustly
reconstruct the photon number distribution of a quantum state. The methodology
is applied experimentally in a 9-port loop detector operating at a
telecommunications wavelength and compared directly to the approach whereby
only the number of photon-counts is used to reconstruct the input distribution.
The signature approach is shown to be more robust against calibration errors,
exhibit reduced statistical uncertainty, and reduced reliance on a-priori
assumptions about the input state.
