Complementarity in categorical quantum mechanics
Quantum Physics
2016-03-03 v2 Mathematical Physics
Category Theory
math.MP
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.
Cite
@article{arxiv.1009.2007,
title = {Complementarity in categorical quantum mechanics},
author = {Chris Heunen},
journal= {arXiv preprint arXiv:1009.2007},
year = {2016}
}
Comments
15 pages; removed incorrect lemma and its dependents