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. 7 References 8

A quantum measurement can be described by a set of matrices, one for each possible outcome, which represents the probability operator-valued measure (POVM) of the sensor. Efficient protocols of POVM extraction for arbitrary sensors are required. We present the first experimental POVM reconstruction that takes explicit advantage of a quantum resource, i.e. nonclassical correlations with an ancillary state. POVM of a photon-number-resolving detector is reconstructed by using strong quantum correlations of twin-beams generated by parametric downconversion. Our reconstruction method is more statistically robust than POVM reconstruction methods that use classical input states.PACS numbers: 42.50. Dv, 42.50.Ar, 03.65.Ta, 85.60.Gz Measurements are at heart of scientific method, because they allow to gauge observables in experimental tests, leading either to the confirmation or to the ruling out of the scientific hypothesis. In quantum mechanics measurements play a critical role because they connect the abstract description of quantum phenomena in Hilbert space to observable events. In the process of measurement, a quantum mechanical object interacts with a measurement device, and a measurement outcome is a result of such interaction. A complete quantum mechanical description of a measurement device is its positive operator-valued measure (POVM). In the quantum realm, sensor calibration corresponds to determining its POVM. In the last decade, the rapid development of innovative quantum technologies promoted POVMs from being an abstract theoretical tool to the experimental realm. In particular, precise and fully quantum characterization techniques for sensors [1-4] play a critical role for the implementation of quantum information processing, metrology and imaging [5][6][7][8][9][10][11][12][13][14][15][16], as well as tomography of states [17][18][19][20][21][22][23][24] and operations [25][26][27][28][29][30]. Quantum sensor characterization can be thus seen as a simultaneous measurement of multiple parameters, therefore the efficiency of such measurement is of utmost importance. However, POVM extraction has been experimentally pursued by brute force methods so far, i.e. by probing sensors with a suitably large set of interrelated input signals, classical states, yielding slow convergence [2,3]. It was shown [1] that taking advantage of quantum resources, e.g. entanglement, can improve convergence beyond the traditional methods. Here, we present the first experimental POVM's reconstruction that explicitly uses a quantum resource, i.e. nonclassical correlations with an ancillary state [31]. Our experiment represents a major step forward towards quantum mechanical treatment of sensors: it demonstrates reconstruction of an inherently quantum measure of an arbitrary detector's performance-its POVM-by realizing for the first time the method of ref. [1].A POVM is defined as a set of operators (matrices) Π n that give the probability of the measurement outcomes via the Born Rule p n = Tr [ Π n ], where is the density opera...

This paper's purpose is to review the results recently\ud obtained in the Quantum Optics labs of the National\ud Institute of Metrological Research (INRIM) in the\ud eld of single- and few-photon detectors calibration,\ud from both the classical and quantum viewpoint.\ud In the rst part of the paper is presented the calibra-\ud tion of a single-photon detector with absolute meth-\ud ods, while in the second part we focus on photon-\ud number-resolving detectors, discussing both the clas-\ud sical and quantum characterization of such devices

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