Quantum nonlocality of high-dimensional multipartite systems

Abstract

I discuss the recent results on quantum nonlocality, in terms of Bell inequalities and/or Greenberg-Horne-Zeilinger nonlocality, for higher-dimensional multipartite systems. Nonlocality of a bipartite high-dimensional system can be shown by using Gisin-Peres theorem but this is only of two-dimensional nature as measurements are performed in two-dimensional subspaces to obtain the optimal nonlocality. Recently, the investigations of genuinely high-dimensional nonlocality have been made. For those, it has been notified that the measurements are high-dimensional but just partially complementary in the sense that they are mutually biased, instead of unbiased. My talk discusses them and new Bell inequalities which are most violated if unbiased measurements are employed. It also includes the generalization of Greenberger-Horne-Zeilinger nonlocality to multipartite high dimensional systems.