Some Recent Progresses in Quantum Tomography Realized at INRIM

We present some Quantum Tomography related results recently obtained in the Quantum Optics labs of the National Institute of Metrological Research (INRIM). Initially we describe the first experimental implementation of a new protocol for the reconstruction of a photon-number-resolving (PNR) detector s POVM (Positive Operator-Valued Measure): such a protocol, exploiting the strong quantum correlations of an ancillary state, results more robust and efficient than its classical counterparts. The second part of the paper focuses on the quantum characterization of a transition-edge sensor (TES) based PNR detector, i.e. the experimental tomography of the POVM of a TES, with a method based on a quorum of coherent probes: we show the reconstruction of the POVM elements up to 11 detected photons and 100 incoming photons, demonstrating the linearity of such a device. Finally, we present a method for the experimental reconstruction of the modal structure of multimode optical fields exploiting a single measurement of higher-order photon number autocorrelation functions. We show our reconstructions of up to three different modes per optical state, demonstrating the excellent agreement with the theoretical predictions and the robustness of our method itself.