A substructural logic for quantum measurements
Abstract
This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic structures include a binary relation that expresses orthogonality between elements and enables the definition of an operation that generalizes the projection operation in Hilbert spaces. The language has a unitary connective, a sort of negation, and two dual binary connectives that are neither commutative nor associative, sorts of conjunction and disjunction. This provides a logic for quantum measurements whose proof theory is aesthetically pleasing.
Cite
@article{arxiv.2212.02833,
title = {A substructural logic for quantum measurements},
author = {Daniel Lehmann},
journal= {arXiv preprint arXiv:2212.02833},
year = {2023}
}
Comments
38 pages, draft to be submitted, comments and remarks welcomed to lehmann@cs.huji.ac.il. This is a corrected, lean, streamlined version of the previous version