MiS Preprint Repository

We study the nonlocality of high dimensional quantum systems based on quantum entanglement and projection. First, a quantitative relationship between the maximal expectation value $B$ of Bell operators and the quantum entanglement concurrence $C$ is obtained for even dimensional pure and mixed states, with the lower bounds of $B$ governed by $C$. Second, by projecting the high dimension bipartite and tripartite quantum states to "two-qubit" and "three-qubit" quantum states, respectively, the nonlocality of the high dimensional quantum states is revealed by the violations of Bell inequalities of the projected qubits states. If the projected qubits states violate Bell inequalities but the violation is less than certain values, there exist kinds of "hidden" nonlocality of the high dimensional states, we call it locally-preprocessed-allowed nonlocality. Examples of high dimensional isotropic states are presented to illustrate the relationship between nonlocality and locally-preprocessed-allowed nonlocality.