Exponential Modalities and Complementarity (extended abstract)

Autor:	Cockett, Robin, Srinivasan, Priyaa Varshinee
Rok vydání:	2021
Předmět:	Mathematics - Category Theory Computer Science - Logic in Computer Science
Zdroj:	EPTCS 372, 2022, pp. 207-220
Druh dokumentu:	Working Paper
DOI:	10.4204/EPTCS.372.15
Popis:	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. Comment: In Proceedings ACT 2021, arXiv:2211.01102. A full version of this paper, containing all proofs, appears at arXiv:2103:05191
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.05191 Zobrazit plný text záznamu View this record from Arxiv