Nonlocality distillation for high-dimensional correlated boxes

Abstract

Most of the existing distillation protocols only work for binary-input binary-output nonlocal boxes (two-dimensional boxes), and they cannot be generalized to the binary-input multi-output nonlocal boxes (high-dimensional boxes) in a trivial way. We will design some comparator-based protocols to distill high-dimensional nonlocal boxes. Our protocols are more powerful and universal than the previous ones in the sense that they can distill the arbitrary-dimensional boxes rather than the limited two-dimensional ones. The initial nonlocalities and the wiring manners between the boxes are two main factors deciding the distillation efficiency.