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7 Contextual logic for quantum systems

Graciela Domenech, See Profile, Available From Graciela Domenech, Héctor Freytes

Published Jan 1, 2005• 27 citations
OpenAlex

Abstract

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Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes.
This paper introduces the Quantum Contextual Topos (QCT), a novel framework that extends traditional quantum logic by embedding contextual elements within a topos-theoretic structure. This framework seeks to provide a classically-obedient tool for exploring the logical foundations of quantum mechanics. The QCT framework aims to address the limitations of classical quantum logic, particularly its challenges in capturing the dynamic and contextual nature of quantum phenomena. By integrating modal operators and classical propositional logic within a topos structure, the QCT offers a unified approach to modeling quantum systems. The main result of this work is demonstrating that the internal logic of QCT corresponds to a form of classical propositional polymodal logic. We do this by generalizing Stone's Representation Theorem for a specific case of polymodal algebras and their underlying Stone Spaces.