Geometric-Phase (Pancharatnam-Berry) Correction for Time-Bin Photonic Qudits: A Calibration and Feed-Forward Algorithm

• URL: http://arxiv.org/abs/2604.27009v1
• Date: Wed, 29 Apr 2026 09:18:02 GMT
• Title: Geometric-Phase (Pancharatnam-Berry) Correction for Time-Bin Photonic Qudits: A Calibration and Feed-Forward Algorithm
• Abstract summary: We develop a geometric-phase framework for time-bin photonic qudits.<n>We propose a practical calibration and feed-forward algorithm for separating and compensating geometric, dynamical, and technical phase contributions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a geometric-phase framework for time-bin photonic qudits and propose a practical calibration and feed-forward algorithm for separating and compensating geometric (Pancharatnam-Berry), dynamical, and technical phase contributions. Working directly in the time-bin basis, we use a parallel-transport gauge so that geometric phases appear as experimentally identifiable interferometric offsets, while all phase contributions enter a bin-resolved diagonal transformation. We model state preparation by cascaded unbalanced Mach-Zehnder interferometers and give closed-form amplitudes for arbitrary splitting ratios and phases, noting that single-port monitoring requires post-selection and renormalization. We then give an interferometric tomography recipe based on adjacent-bin scans, with a Fourier-basis cross-check, and a multi-mode numerical case study that separates total, dynamical, and geometric phases and demonstrates feed-forward compensation. The protocol uses standard components, including tunable UMZIs, phase shifters or EOMs, and single-photon detectors, together with routine phase sweeps. It is intended for small to moderate dimensions, approximately d up to 10, and provides a scalable route toward phase-stable high-dimensional temporal encoding for quantum communication and photonic processing.

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