Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution

TL;DR

This paper presents a fast, efficient method for high-dimensional compressive imaging of bi-photon probability distributions using Hadamard transforms, enabling rapid reconstruction of multi-million dimensional images.

Contribution

It introduces a Kronecker-based fast-Hadamard-transform approach for compressive sensing in joint quantum systems, significantly reducing reconstruction time for extremely high-dimensional data.

Findings

Reconstructed a 16.8 million-dimensional image in under 10 minutes.

Successfully measured a 3.2 million-dimensional bi-photon probability distribution.

Marginal distributions improve the accuracy of joint distribution reconstructions.

Abstract

We demonstrate how to efficiently implement extremely high-dimensional compressive imaging of a bi-photon probability distribution. Our method uses fast-Hadamard-transform Kronecker-based compressive sensing to acquire the joint space distribution. We list, in detail, the operations necessary to enable fast-transform-based matrix-vector operations in the joint space to reconstruct a 16.8 million-dimensional image in less than 10 minutes. Within a subspace of that image exists a 3.2 million-dimensional bi-photon probability distribution. In addition, we demonstrate how the marginal distributions can aid in the accuracy of joint space distribution reconstructions.