# Quantum channel correction with twisted light using compressive sensing

## TL;DR

This paper demonstrates that compressive sensing can effectively estimate and correct atmospheric turbulence effects on high-dimensional quantum channels using classical light, enhancing free-space optical communication.

## Contribution

It introduces a novel application of compressive sensing for quantum channel correction with twisted light, including a numerical simulation demonstrating its effectiveness.

## Key findings

- High fidelity in corrected states
- Reduced atmospheric turbulence effects
- Quantified non-separability post-correction

## Abstract

Compressive sensing is used to perform high-dimensional quantum channel estimation with classical light. As an example, we perform a numerical simulation for the case of a three-dimensional classically non-separable state that is propagated through atmospheric turbulence. Using singular value thresholding algorithm based compressive sensing, we determine the channel matrix, which we subsequently use to correct for the atmospheric turbulence induced distortions. As a measure of the success of the procedure, we calculate the fidelity and the trace distance of the corrected density matrix with respect to the input state, and compare the results with those of the density matrix for the uncorrected state. Furthermore, we quantify the amount of classical non-separability in the density matrix of the corrected state by calculating its negativity. The results show that compressive sensing could contribute in the development and implementation of free-space quantum and optical communication systems.