Related papers: A substructural logic for quantum measurements

A substructural logic for quantum measurements

URL: http://arxiv.org/abs/2212.02833v2
Date: Tue, 18 Jul 2023 13:21:50 GMT
Title: A substructural logic for quantum measurements
Authors: Daniel Lehmann
Abstract summary: 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.
Score: 1.8782750537161614
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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