Nonlocal distillation based on multisetting Bell inequality

Abstract

Inspired by the recent works of Foster and Brunner, we present a nonlocality distillation protocol for two three-level (qutrit) systems in the framework of generalized nonsignaling theories. Our protocol is based on a three-setting Bell inequality. It works efficiently for a specific class of three-input-three-output nonlocal boxes. In the asymptotic limit, all these nonlocal boxes can be distilled to the maximally nonlocal box defined by the inequality and nonsignaling constraints. Then we introduce a contracting protocol that reduces these boxes to the so-called "correlated nonlocal boxes." As a result, our three-input-three-output nonlocal boxes also make communication complexity trivial and appear very unlikely to exist in nature. © 2012 American Physical Society.