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Quantum Simulation

Complementarity in categorical quantum mechanics

arXiv

Authors: Chris Heunen

Year

2010

Paper ID

11337

Status

Preprint

Abstract Read

~2 min

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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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We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1009.2007 [2] arXiv https://arxiv.org/abs/1009.2007 [3] Publisher https://arxiv.org/abs/1009.2007

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