Entanglement-assisted calibration of a photon-number-resolving detector

Abstract

Here we present the first experimental entanglement-assisted quantum characterization of an unknown photon-number-resolving detector, i.e. the reconstruction of its positive operator-valued measure (POVM), obtained by exploiting the quantum correlations of a twin-beam generated by parametric down conversion (PDC). Theoretical frameworkHere we present the first experimental entanglement-assisted quantum characterization of an unknown photon-numberresolving (PNR) detector, obtained by exploiting the quantum correlations of a twin-beam generated by parametric down conversion (PDC): one beam is revealed by the detector under calibration (DUC), whereas the other one is sent to a quantum tomographer (T). The calibration of a quantum apparatus corresponds to determining its positive operatorvalued measure (POVM), i.e. the set of operators Π n providing the probability of the measurement outcomes via the Born rule p n = Tr [ρ Π n ], where ρ is the density operator describing the system being measured. The reconstruction of a detector POVM can be achieved by the inversion of the Born Rule [1], but recently another calibration scheme was proposed [2], based on quantum correlations of a bipartite system whose parts are sent to the DUC and to a tomographer. This scheme, both more reliable and less demanding, is a clear example of ancilla-assisted quantum scheme, where quantum correlations play a key role in order to improve both precision and stability. To perform the tomographic reconstruction needed here [2], we make use of a maximum-likelihood based method [3,4] exploiting on/off detectors with variable quantum efficiency to reconstruct the diagonal elements of the density matrix of quantum optical states. This method has been tested in different regimes [5] and generalized to the bipartite case [6], improved with the addition of a proper energy constraint [7] and extended also to the off-diagonal elements of the density matrix [8,9]: now it will be applied also to this ancilla-assisted POVM reconstruction experiment. Experimental setup and resultsThe experimental setup (Fig. 1) is composed by a 400 nm mode-locked laser pumping a LiIO 3 crystal in order to produce degenerate and non-collinear Type-I Parametric Down Conversion. One of the selected branches of degenerate PDC (at 800 nm) is sent to the Tomographer, composed by a calcite polarizer, a pinhole, an Interference Filter (20 nm of Full Width at Half Maximum) and a fibre coupler connected by a multimode fibre to a Si-Single Photon Avalanche Diode (SPAD). Being the down converted photons characterized by the same polarization, the polarizer is used to change step by step the efficiency of the tomographer. The correlated branch is sent to the PNR DUC, that is constituted by a 50% − 50% multimode fibre beam splitter whose outputs are connected to two Si-SPADs, while the input port is again connected to the same coupling system described above (it is straightforward to notice that our PNR is able to discriminate between 0, 1 and 2-or-more photons detected per pulse). Th...