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Entropy 2017, 19(5), 220; doi:10.3390/e19050220

A Functorial Construction of Quantum Subtheories

1
Department of Mathematics, University of Illinois at Urbana-Champain, Urbana, IL 61801, USA
2
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
*
Author to whom correspondence should be addressed.
Academic Editors: Giacomo Mauro D’Ariano, Andrei Khrennikov and Massimo Melucci
Received: 2 March 2017 / Revised: 3 May 2017 / Accepted: 4 May 2017 / Published: 11 May 2017
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
View Full-Text   |   Download PDF [379 KB, uploaded 11 May 2017]   |  

Abstract

We apply the geometric quantization procedure via symplectic groupoids to the setting of epistemically-restricted toy theories formalized by Spekkens (Spekkens, 2016). 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 of the toy theories to the Frobenius algebra of stabilizer quantum mechanics. View Full-Text
Keywords: categorical quantum mechanics; geometric quantization; epistemically-restricted theories; Frobenius algebras categorical quantum mechanics; geometric quantization; epistemically-restricted theories; Frobenius algebras
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Contreras, I.; Duman, A.N. A Functorial Construction of Quantum Subtheories. Entropy 2017, 19, 220.

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