On precision in HOM interferometer delay time measurements and estimation of photon loss probability in an interferometer

An analysis of the precision of temporal delay estimation in a Hong–Ou–Mandel (HOM) interferometer is carried out via the error propagation formula and the classical Fisher information. The study finds delay times characterized by a minimum precision, where precision is defined as the standard deviation of the estimated delay, and those for which this precision is a minimal fraction of the delay time itself. The temporal delay is measured in units set by the location of the inflection point on the HOM coincidence dip, with the corresponding delay time in the considered models depending solely on the biphoton spectrum width. The paper also discusses the estimation of photon loss probability in an interferometer, which is based on the temporal delay estimate that possesses minimum variance.