The exponential modalities of linear logic have been used by various authors to model infinite-dimensional quantum systems. This paper explains how these modalities can also give rise to the complementarity principle of quantum mechanics. The paper uses a formulation of quantum systems based on dagger-linear logic, whose categorical semantics lies in mixed unitary categories, and a formulation of measurement therein. The main result exhibits a complementary system as the result of measurements on free exponential modalities. Recalling that, in linear logic, exponential modalities have two distinct but dual components, ! and ?, this shows how these components under measurement become "compacted" into the usual notion of complementary Frobenius algebras from categorical quantum mechanics.
翻译:各作者利用线性逻辑的指数模式来模拟无限量子系统。本文解释了这些模式如何也能产生量子力学的互补性原则。本文使用了基于匕首线性逻辑的量子系统的配方,其绝对语义以混合的单一类别为基础,其中的测量公式。主要结果显示了通过测量自由指数模式而形成的一个互补系统。回顾在线性逻辑中,指数模式有两个不同但双重的成分, 以及? 这表明测量中的这些成分是如何“合成”成从绝对量子力学中补充Frobenius代数的通常概念的。