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Trapped Ion Quantum Computing

A Formal Theory for Finite-Dimensional Possibilistic Quantum Mechanics

arXiv

Authors: Olivier Brunet

Year

2026

Paper ID

15797

Status

Preprint

Abstract Read

~2 min

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Abstract

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of model theory in our study. In particular, we show that our formal theory is complete, meaning that it entirely determines the behaviour of quantum systems. Moreover, we provide a characterization of the models of our formal theory, thus providing new insights in the study of hidden variable models of quantum theory.

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This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
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In this work, we present a logical formalism for reasoning about quantum systems in finite dimension.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2602.16368 [2] arXiv https://arxiv.org/abs/2602.16368 [3] Publisher https://arxiv.org/abs/2602.16368

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