Complementarity in Categorical Quantum Mechanics

Foundations of Physics 42 (7):856-873 (2012)
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We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a ‘point-free’ definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras



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The Problem of Hidden Variables in Quantum Mechanics.Simon Kochen & E. P. Specker - 1967 - Journal of Mathematics and Mechanics 17:59--87.
The Logical Analysis of Quantum Mechanics.Edward MacKinnon - 1974 - British Journal for the Philosophy of Science 25 (4):352-358.
The meaning of complementarity.Carsten Held - 1994 - Studies in History and Philosophy of Science Part A 25 (6):871-893.

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