Nonlocal distillation based on multisetting Bell inequality

Abstract

Inspired by the recent works of Foster et al. [Phys. Rev. Lett. 102, 120401 (2009)] and Brunner et al. [Phys. Rev. Lett. 102, 160403 (2009)], 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.