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An analogous model system for high-dimensional quantum entanglement isproposed, based on the angular and radial degrees of freedom of the improvedLaguerre Gaussian mode. Experimentally, we observed strong violations of theBell-CGLMP inequality for maximally non-separable states of dimension 2 through10. The results for violations in classical non-separable state are in verygood agreement with quantum instance, which illustrates that our scheme can bea useful platform to simulate high-dimensional non-local entanglement.Additionally, we found that the Bell measurements provide sufficient criteriafor identifying mode separability in a high-dimensional space. Similar to thetwo-dimensional spin-orbit non-separable state, the proposed high-dimensionalangular-radial non-separable state may provide promising applications forclassical and quantum information processing.

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