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Entropy 2017, 19(5), 220;

A Functorial Construction of Quantum Subtheories

Department of Mathematics, University of Illinois at Urbana-Champain, Urbana, IL 61801, USA
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)
Full-Text   |   PDF [379 KB, uploaded 11 May 2017]   |  


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

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