Photonic quantum information processing using the frequency continuous variable of single photons

The celebrated Hong–Ou–Mandel effect illustrates the richness of two-photon interferometry. In this work, we demonstrate that this extends to the realm of time–frequency interferometry. Taking advantage of the mathematical analogy which can be drawn between the frequency and quadrature degrees of freedom of light when there is a single photon in each auxiliary mode, we consider the equivalent of the Hong–Ou–Mandel effect in the frequency domain. In this setting, the n-Fock state becomes equivalent to a single-photon state with a spectral wave function given by the nth Hermite–Gauss function and destructive interference corresponds to vanishing probability of detecting single photons with an order one Hermite–Gauss spectral profile. This compelling analogy motivates us to propose an interferometric strategy that uses a frequency-engineered two-photon state to achieve enhanced phase precision that scales inversely with the number of modes. Finally, we generalize the Gaussian Boson sampling model to time–frequency degrees of freedom of single photons. Through all these applications, we emphasize that distinct types of quantum resources and degrees of freedom can yield identical statistical outcomes and information processing capabilities.