Single-photon-added coherent states: estimation of parameters and fidelity of the optical homodyne detection

The travelling modes of single-photon-added coherent states (SPACS) are characterized by using optical homodyne tomography. Given a set of experimentally measured quadrature distributions, we estimate parameters of the state and also extract information about the detector efficiency. The method used is minimal distance estimation between theoretical and experimental quantities, which additionally allows to evaluate the precision of the estimated parameters. Given the experimental data, we also estimate the lower and upper bounds on fidelity. The results are believed to encourage a more precise engineering and detection of SPACS.