Dzhafarov Ehtibar N, Cervantes Víctor H, Kujala Janne V
Psychological Sciences, Purdue University, West Lafayette, IN, USA
Psychological Sciences, Purdue University, West Lafayette, IN, USA.
Philos Trans A Math Phys Eng Sci. 2017 Nov 13;375(2106). doi: 10.1098/rsta.2016.0389.
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions of the context-sharing random variables. We propose to represent any system of measurements in a canonical form and to consider the system contextual if and only if its canonical representation is contextual. As an illustration, we establish a criterion for contextuality of the canonical system consisting of all dichotomizations of a single pair of content-sharing categorical random variables.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
表示测量的随机变量，广义上理解为包括对任何输入的任何响应，它们构成一个系统，其中每个随机变量都由其内容（它所测量的东西）及其上下文（记录它的条件）唯一标识。当且仅当两个随机变量共享一个上下文时，它们才是联合分布的。在系统的规范表示中，所有随机变量都是二元的，并且每对共享内容的随机变量都有一个唯一的最大耦合（强加于它们的联合分布，以使它们以最大可能概率重合）。如果这些最大耦合与共享上下文的随机变量的联合分布不兼容，则该系统是上下文相关的。我们建议以规范形式表示任何测量系统，并且当且仅当其规范表示是上下文相关时，才认为该系统是上下文相关的。作为一个例证，我们为包含一对共享内容的分类随机变量的所有二分法的规范系统建立了一个上下文相关性标准。本文是主题为“第二次量子革命：基础问题”的特刊的一部分。
