Bell`s Theorem with Many Observables

Abstract

Quantum nonlocality implies a quantum correlation that no local realistic theories can simulate. It is at the heart of quantum mechanics and also plays essential roles in quantum information processing. In 1964, Bell showed the nonlocality for a very simple system of two qubits by using dichotomic observables. In this work, we investigate the quantum nonlocality for a complex system, which is a multipartite. For the purpose, we derive generic Bell inequalities consisting of many measurements per party, each measurement having many possible outcomes. We show that it is violated by quantum mechanics for a tripartite system, each subsystem being in a two or four dimension.