We address the quantum characterization of photon counters based on transition-edge sensors (TESs) and present the first experimental tomography of the positive operator-valued measure (POVM) of a TES. We provide the reliable tomographic reconstruction of the POVM elements up to 11 detected photons and M = 100 incoming photons, demonstrating that it is a linear detector.

Well characterized photon number resolving detectors are a requirement for many applications ranging from quantum information and quantum metrology to the foundations of quantum mechanics. This prompts the necessity for reliable calibration techniques at the single photon level. In this paper we propose an innovative absolute calibration technique for photon number resolving detectors, using a pulsed heralded photon source based on parametric down conversion. The technique, being absolute, does not require reference standards and is independent upon the performances of the heralding detector. The method provides the results of quantum efficiency for the heralded detector as a function of detected photon numbers. Furthermore, we prove its validity by performing the calibration of a Transition Edge Sensor based detector, a real photon number resolving detector that has recently demonstrated its effectiveness in various quantum information protocols.

Transition Edge Sensors (TESs) are characterized by the intrinsic figures of merit to resolve both the energy and the statistical distribution of the incident photons. These properties lead TES devices to become the best single photon detectors for quantum technology experiments. For a TES based on titanium and gold, has been reached, at telecommunication wavelength, an unprecedented intrinsic energy resolution (0.113 eV). The uncertainty analysis of both energy resolution and photon state assignment has been discussed. The thermal properties of the superconductive device have been studied by fitting the bias curves to evaluate the theoretical limit of the energy resolution.