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

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THE LOGIC OF QUANTUM MECHANICS – TAKE II

BOB COECKE

Abstract. We put forward a new take on the logic of quantum mechanics, following Schrödinger’s point of view that it is composition which makes quantum theory what it is, rather than its particular propositional structure due to the existence of superpositions, as proposed by Birkhoff and von Neumann. This gives rise to an intrinsically quantitative kind of logic, which truly deserves the name ‘logic’ in that it also models meaning in natural language, the latter being the origin of logic, that it supports automation, the most prominent practical use of logic, and that it supports probabilistic inference.

§1. The physics and the logic of quantum-ish logic. In 1932 John von Neumann formalized ...

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