A More Efficient Contextuality Distillation Protocol

Abstract

Based on the fact that both nonlocality and contextuality are resource theories, it is natural to ask how to amplify them more efficiently. In this paper, we present a contextuality distillation protocol which produces an n-cycle box B ∗ B ′ from two given n-cycle boxes B and B ′. It works efficiently for a class of contextual n-cycle (n ≥ 4) boxes which we termed as “the generalized correlated contextual n-cycle boxes”. For any two generalized correlated contextual n-cycle boxes B and B ′, B ∗ B ′ is more contextual than both B and B ′. Moreover, they can be distilled toward to the maximally contextual box C H n as the times of iteration goes to infinity. Among the known protocols, our protocol has the strongest approximate ability and is optimal in terms of its distillation rate. What is worth noting is that our protocol can witness a larger set of nonlocal boxes that make communication complexity trivial than the protocol in Brunner and Skrzypczyk (Phys. Rev. Lett. 102, 160403 2009), this might be helpful for exploring the problem that why quantum nonlocality is limited.