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arXiv · 1009.2007

Complementarity in categorical quantum mechanics

Chris Heunen
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Abstract

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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Chris Heunen. 2010-09-10. Complementarity in categorical quantum mechanics. https://doi.org/10.1007/s10701-011-9585-9

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