# Classical simulation of high-dimensional entanglement by non-separable angular--radial modes

## TL;DR

This paper demonstrates a classical simulation platform for high-dimensional quantum entanglement using non-separable angular-radial modes of Laguerre Gaussian beams, showing strong Bell inequality violations and potential for quantum information applications.

## Contribution

It introduces a novel classical model system for high-dimensional entanglement using angular and radial degrees of freedom, matching quantum violations and identifying mode separability criteria.

## Key findings

- Strong Bell-CGLMP inequality violations observed for dimensions 2 to 10.
- Classical non-separable states closely match quantum violation results.
- Bell measurements effectively identify mode separability in high-dimensional space.

## Abstract

An analogous model system for high-dimensional quantum entanglement is proposed, based on the angular and radial degrees of freedom of the improved Laguerre Gaussian mode. Experimentally, we observed strong violations of the Bell-CGLMP inequality for maximally non-separable states of dimension 2 through 10. The results for violations in classical non-separable state are in very good agreement with quantum instance, which illustrates that our scheme can be a useful platform to simulate high-dimensional non-local entanglement. Additionally, we found that the Bell measurements provide sufficient criteria for identifying mode separability in a high-dimensional space. Similar to the two-dimensional spin-orbit non-separable state, the proposed high-dimensional angular-radial non-separable state may provide promising applications for classical and quantum information processing.