Numerical analysis of single-photon phase noise via time-resolved two-photon interference

Measuring the phase stability of single photons is essential for evaluating performance in various phase-based quantum applications, yet systematic methodologies for quantitative characterization remain underexplored. In this work, we numerically demonstrate that time-resolved two-photon interference can be effectively utilized to estimate the phase noise of single photons. Our simulations reveal that as phase noise increases, the interference visibility decreases, causing the joint detection probability to approach the non-interfering classical envelope. Furthermore, we verify that the power spectral density (PSD) of the phase noise can be reconstructed using a derived mathematical relationship. This approach establishes a direct quantitative link between measurable interference patterns and the underlying statistical phase fluctuations. This method provides a practical framework for characterizing single-photon phase stability, offering significant potential for enhancing quantum technologies such as quantum key distribution and sensing.