High-Dimensional Methods for Quantum Homodyne Tomography

TL;DR

This paper introduces optimized recursive techniques and a Julia package for high-dimensional quantum homodyne tomography, improving state reconstruction accuracy for complex quantum states.

Contribution

It provides refined recursion relations and implementation strategies that enhance the analysis of high-dimensional quantum states in homodyne tomography.

Findings

Mitigates divergences in pattern function calculations.

Enables accurate reconstruction of excited quantum states.

Provides a Julia package for practical data analysis.

Abstract

We provide optimized recursion relations for homodyne tomography. We improve previous methods by mitigating the divergences intrinsic in the calculation of the pattern functions used previously, and detail how to implement the data analysis through Monte Carlo simulations. Our refinements are necessary for the reconstruction of excited quantum states which populate a high-dimensional subspace of the electromagnetic field Hilbert space. We also present a Julia package for the analysis and the reconstruction method.