Time-frequency Talbot effect as Clifford operations on entangled time-frequency Gottesman-Kitaev-Preskill states
Phys. Rev. A 114, 042613 – Published 13 October, 2026
DOI: https://doi.org/10.1103/46qd-jc1v
Abstract
The Talbot effect, a near-field diffraction phenomenon in which a periodic wavefront self-images at regular distances, can be transposed to the time-frequency domain via the spacetime duality between diffraction and dispersive broadening. We exploit this analogy to define the time-frequency (TF) Talbot effect and show that it implements different Clifford operations on TF Gottesman-Kitaev-Preskill (TF-GKP) qubits [Fabre et al., Phys. Rev. A 102, 012607 (2020)], a class of qubit states encoded in the discretized frequency and time-of-arrival degrees of freedom of entangled photon pairs, whose logical basis corresponds to even and odd components of an entangled frequency comb. These states are intrinsically robust against small frequency and temporal displacements, which can be further corrected by linear or nonlinear quantum error-correction schemes. We analyze the role of the comb envelope and peak width relative to the free spectral range, and show that a compromise must be made between the gate fidelity of the Clifford gates induced by TF-Talbot operation and the error-correction capacity of the code. We then demonstrate that the signature of the TF-Talbot effect is directly accessible via the generalized Hong-Ou-Mandel interferometer: all six logical GKP states can be unambiguously distinguished by introducing a frequency shift of half the comb periodicity in one interferometer arm. We conclude with a feasibility analysis based on current experimental technology, identifying the comb finesse as the key figure of merit for both gate performance and correctability. This conclusion extends naturally to quadrature GKP states, where a shear in quadrature phase space is precisely a Talbot effect.
