# Experimental observation of fractional topological phases with photonic qudits

## TL;DR

This paper experimentally demonstrates fractional topological phases in entangled photonic qudits, revealing how local operations induce measurable phase shifts in interference patterns across different dimensions.

## Contribution

It provides the first experimental observation of fractional topological phases in photonic qudits, confirming theoretical predictions for dimensions 2, 3, and 4.

## Key findings

- Measured topological phase shifts match theoretical values
- Demonstrated fractional phases in dimensions 2, 3, and 4
- Used Sagnac interferometer for phase detection

## Abstract

Geometrical and topological phases play a fundamental role in quantum theory. Geometric phases have been proposed as a tool for implementing unitary gates for quantum computation. A fractional topological phase has been recently discovered for bipartite systems. The dimension of the Hilbert space determines the topological phase of entangled qudits under local unitary operations. Here we investigate fractional topological phases acquired by photonic entangled qudits. Photon pairs prepared as spatial qudits are operated inside a Sagnac interferometer and the two-photon interference pattern reveals the topological phase as fringes shifts when local operations are performed. Dimensions $d = 2, 3$ and $4$ were tested, showing the expected theoretical values.