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Complementarity in Categorical Quantum Mechanics

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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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  1. Department of Computer Science, University of Oxford, Oxford, UK

    Chris Heunen

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  1. Chris Heunen
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Correspondence to Chris Heunen.

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Supported by the Netherlands Organisation for Scientific Research (NWO).

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Heunen, C. Complementarity in Categorical Quantum Mechanics. Found Phys 42, 856–873 (2012). https://doi.org/10.1007/s10701-011-9585-9

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  • DOI: https://doi.org/10.1007/s10701-011-9585-9

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