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.
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