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 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 tripartite system. For that purpose, we derive a generic Bell inequality consisting of four observables on each subsystem in high-dimensional Hilbert space. We show that the inequality is violated by quantum mechanics for a generalized Greenberg-Horne-Zeilinger state, each subsystem being in an arbitrary even dimension.