# High-dimension experimental tomography of a path-encoded photon quantum-state

## TL;DR

This paper introduces a resource-efficient method for high-dimensional quantum state tomography of path-encoded photons using a rotating optical Fourier Transform, achieving high fidelity in experimental demonstrations.

## Contribution

The authors develop and experimentally validate a simple, scalable tomography technique for high-dimensional path-encoded photon states, reducing complexity compared to traditional methods.

## Key findings

- Achieved an average fidelity of 0.9852 in reconstructing six-dimensional states.
- Demonstrated the method's effectiveness across various six-dimensional density matrices.
- Performance exceeds or matches existing tomographic techniques for similar systems.

## Abstract

Quantum information protocols often rely on tomographic techniques to determine the state of the system. A popular method of encoding information is on the different paths a photon may take, for example, parallel waveguides in integrated optics. However, reconstruction of states encoded onto a large number of paths is often prohibitively resource intensive and requires complicated experimental setups. Addressing this, we present a simple method for determining the state of a photon in a superposition of d paths using a rotating one-dimensional optical Fourier Transform. We establish the theory and experimentally demonstrate the technique by measuring a wide variety of six-dimensional density matrices. The average fidelity of these with the expected state is as high as 0.9852 +/- 0.0008. This performance is comparable or exceeds established tomographic methods for other types of systems.