测量概率上下文的全可能耦合方法
All-Possible-Couplings Approach to Measuring Probabilistic Context
摘要：
从行为科学到生物学再到量子力学，我们会遇到这样的情况：（i）系统输出几个随机变量以响应几个输入;（ii）对于这些响应中的每一个，只有一些输入可能“直接”影响它们;但是（iii）其他输入通过影响其与其他响应的概率关系为该响应提供“上下文”。这些背景影响是非常不同的，比如说，在经典动力学理论和量子力学的纠缠范式中，它们传统上被解释为代表不同形式的物理决定论。人们可以用数学方法构造具有其他类型的上下文性的系统，无论这些上下文性是否在经验上是可实现的：那些形成经典类型的特例的系统，那些介于经典和量子类型之间的系统，以及那些违反量子类型的系统。我们展示了如何通过研究各种概率耦合集来量化和分类所有逻辑上可能的上下文影响，即，施加在不同（互不相容）输入值下记录的随机输出上的联合分布集合。
英文摘要：
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly" influence them, but (iii) other inputs provide a "context" for this response by influencing its probabilistic relations to other responses. These contextual influences are very different, say, in classical kinetic theory and in the entanglement paradigm of quantum mechanics, which are traditionally interpreted as representing different forms of physical determinism. One can mathematically construct systems with other types of contextuality, whether or not empirically realizable: those that form special cases of the classical type, those that fall between the classical and quantum ones, and those that violate the quantum type. We show how one can quantify and classify all logically possible contextual influences by studying various sets of probabilistic couplings, i.e., sets of joint distributions imposed on random outputs recorded at different (mutually incompatible) values of inputs.
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