指数模态和互补性（扩展摘要）
Exponential Modalities and Complementarity (extended abstract)
摘要：
线性逻辑的指数模态已经被许多作者用来模拟无限维量子系统。本文解释了这些模态如何也可以产生量子力学的互补原理。本文使用了基于匕首线性逻辑的量子系统的公式，其范畴语义在于混合酉范畴，以及其中的测量公式。的主要结果表现出一个互补的系统作为自由指数模式的测量结果。回顾一下，在线性逻辑中，指数模态有两个不同但双重的组成部分，！然后呢？这显示了这些被测量的分量是如何被“压缩”到范畴量子力学中的互补Frobenius代数的通常概念中的。
英文摘要：
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.
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