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arXiv · 2103.05191

Exponential Modalities and Complementarity (extended abstract)

Robin Cockett·Priyaa Varshinee Srinivasan
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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.

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Robin Cockett, Priyaa Varshinee Srinivasan. 2021-03-09. Exponential Modalities and Complementarity (extended abstract). https://doi.org/10.4204/eptcs.372.15

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