Sparsity-Driven Entanglement Detection in High-Dimensional Quantum States

TL;DR

This paper presents a sparsity-driven method using $ ext{l}_1$-regularization to improve detection and certification of high-dimensional quantum entanglement, making the process more scalable and noise-resistant.

Contribution

It introduces a novel $ ext{l}_1$-regularized reconstruction framework for entanglement detection that enhances signal visibility and noise suppression in high-dimensional quantum states.

Findings

Enables certification of higher entanglement dimensionality

Improves signal-to-noise ratio in covariance measurements

Compatible with existing quantum optics platforms

Abstract

The characterization of high-dimensional quantum entanglement is crucial for advanced quantum computing and quantum information algorithms. Traditional methods require extensive data acquisition and suffer from limited visibility due to experimental noise. Here, we introduce a sparsity-driven framework to enhance the detection and certification of high-dimensional entanglement in spatially entangled photon pairs. By applying $\ell_1$-regularized reconstruction to sample covariance matrices obtained from measurements on photons produced via spontaneous parametric down-conversion (SPDC) measurements, we enhance the visibility of the correlation signal while suppressing noise. We demonstrate, using a position-momentum Einstein-Podolsky-Rosen (EPR) entanglement criterion, that this approach enables certification of an entanglement dimensionality that cannot be achieved without regularization. Our method is scalable, simple to use and compatible with existing quantum-optics platforms, thus paves the way for efficient, real-time analysis of high-dimensional quantum states.