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

TL;DR

This paper introduces a geometric-phase framework and a practical calibration algorithm for time-bin photonic qudits, enabling phase separation and compensation using standard components for scalable quantum communication.

Contribution

It presents a novel geometric-phase approach with a calibration and feed-forward algorithm for high-dimensional time-bin photonic qudits, facilitating phase stability in quantum photonics.

Findings

Successfully separates geometric, dynamical, and total phases in simulations.

Demonstrates feed-forward compensation in a multi-mode numerical case study.

Provides a scalable protocol suitable for dimensions up to about 10.

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.