Exponential Modalities and Complementarity (extended abstract)
arXiv:2103.05191 · doi:10.4204/EPTCS.372.15
Abstract
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.
In Proceedings ACT 2021, arXiv:2211.01102. A full version of this paper, containing all proofs, appears at arXiv:2103:05191