On the Modal Logic of the Non-orthogonality Relation Between Quantum States

Abstract

It is well known that the non-orthogonality relation between the states of a quantum system is reflexive and symmetric, and the modal logic \ is sound and complete with respect to the class of sets each equipped with a reflexive and symmetric binary relation. In this paper, we consider two properties of the non-orthogonality relation: Separation and Superposition. We find sound and complete modal axiomatizations for the classes of sets each equipped with a reflexive and symmetric relation that satisfies each one of these two properties and both, respectively. We also show that the modal logics involved are decidable.

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Shengyang Zhong
Peking University

References found in this work

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Modal Logic.Alexander Chagrov - 1997 - Oxford, England: Oxford University Press.
The Logic of Quantum Mechanics.Garrett Birkhoff & John von Neumann - 1937 - Journal of Symbolic Logic 2 (1):44-45.
Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.

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