Optimal violation of a Bell inequality in two-dimensional state spaces for an asymmetric orbital angular momentum system

The symmetric orbital angular momentum (OAM) entanglement in the subspace of { ± ℓ} has been extensively exploited in quantum information science. Here we investigate instead the Bell inequalities for the two-dimensional subspace spanned by asymmetric OAM modes of ℓ 1 and ℓ 2 , usually corresponding to the quantum property of nonmaximal entanglement. We demonstrate, both theoretically and experimentally, the optimal violation of a suitable Clauser-Horne-Shimony-Holt Bell inequality for the asymmetric OAM modes, thus manifesting the entanglement for asymmetric OAM states space.