A Functorial Construction of Quantum Subtheories
Mathematical Physics
2017-06-07 v1 Information Theory
math.IT
math.MP
Symplectic Geometry
Abstract
We apply the geometric quantization procedure via symplectic groupoids proposed by E. Hawkins to the setting of epistemically restricted toy theories formalized by Spekkens. In the continuous degrees of freedom, this produces the algebraic structure of quadrature quantum subtheories. In the odd-prime finite degrees of freedom, we obtain a functor from the Frobenius algebra in \textbf{Rel} of the toy theories to the Frobenius algebra of stabilizer quantum mechanics.
Keywords
Cite
@article{arxiv.1705.02971,
title = {A Functorial Construction of Quantum Subtheories},
author = {Ivan Contreras and Ali Nabi Duman},
journal= {arXiv preprint arXiv:1705.02971},
year = {2017}
}
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19 pages