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Logic and Algebraic Structures in Quantum Computing by Valentina Harizanov, Ali Eskandarian, Jennifer Chubb

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TOPOS-BASED LOGIC FOR QUANTUM SYSTEMS AND BI-HEYTING ALGEBRAS

ANDREAS DÖRING

Abstract. To each quantum system, described by a von Neumann algebra of physical quantities, we associate a complete bi-Heyting algebra. The elements of this algebra represent contextualised propositions about the values of the physical quantities of the quantum system.

§1.Introduction. Quantum logic started with Birkhoff and von Neumann’s seminal article [4]. Since then, non-distributive lattices with an orthocomplement (and generalisations thereof) have been used as representatives of the algebra of propositions about the quantum system at hand. There are a number of well-known conceptual and interpretational problems with this kind of ‘logic’. For review of standard ...

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