Certification of photon Fock states using second-order nonlinearity

Abstract

Certifying whether a photon Fock state is present or not while preserving its quantum state is an important task that proves useful in quantum technologies. The existing methods to perform such task apply to single photons only and consume costly quantum resources. In this paper, we propose a resource-efficient scheme for certification of an arbitrary (nonvacuum) photon Fock state by using second-order nonlinearity. In particular, we utilize the correlations in both photon number and polarization of a stimulated parametric downconversion process to herald the presence and the quantum state of an incoming Fock state. The proposed scheme works excellently with a near perfect certification fidelity even when using nonideal photodetectors. We then compare our scheme with the existing ones taking into account relevant figures of merit for each method. We also present applications of our scheme in overcoming transmission loss of photons in quantum channels as well as in preparation of NOON states, $(|N\ensuremath{\rangle}|0\ensuremath{\rangle}+|0\ensuremath{\rangle}|N\ensuremath{\rangle})/\sqrt{2}$. Our paper introduces to the optical toolbox a practical technique that is beneficial for quantum communication and quantum metrology.