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Mathematics > Category Theory

arXiv:2103.05191v2 (math)
[Submitted on 9 Mar 2021 (v1), last revised 3 Nov 2022 (this version, v2)]

Title:Exponential Modalities and Complementarity (extended abstract)

Authors:Robin Cockett (University of Calgary), Priyaa Varshinee Srinivasan (University of Calgary)
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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.
Comments: In Proceedings ACT 2021, arXiv:2211.01102. A full version of this paper, containing all proofs, appears at arXiv:2103:05191
Subjects: Category Theory (math.CT); Logic in Computer Science (cs.LO)
Cite as: arXiv:2103.05191 [math.CT]
  (or arXiv:2103.05191v2 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2103.05191
Journal reference: EPTCS 372, 2022, pp. 207-220
Related DOI: https://doi.org/10.4204/EPTCS.372.15

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 9 Mar 2021 02:52:54 UTC (97 KB)
[v2] Thu, 3 Nov 2022 14:18:49 UTC (37 KB)
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