Time-Frequency Grid States for Reconstruction and Correction of Channel-Induced Distortion in Entangled Photons

Characterization of time-frequency (TF) quantum states requires reliable reconstruction of their TF distributions. However, imperfect transmission or measurement channels can distort reconstructed joint spectral intensities (JSIs), especially when the underlying perturbation mechanism is unknown. Here, we experimentally demonstrate a reconstruction and correction framework that uses a TF grid state as an intrinsic frequency-domain reference. By analyzing the displacement of the grid points, a Gaussian process regression model is employed to reconstruct a correction mapping for the nonlinear coordinate deformation without assuming a prior physical model of the distortion. The learned mapping reduces the residual coordinate deviation of the TF grid state by approximately a factor of 11 and, when applied to an independent frequency-entangled test state, improves the Gaussian-shape fidelity from 76.2% to 90.0%. These results establish TF grid states as practical metrological resources for diagnosing and correcting distortions in TF quantum systems, providing a pathway toward distortion-resilient quantum communication and high-dimensional quantum information processing.