A functorial construction of quantum subtheories

Ivan Contreras; Ali Nabi Duman

doi:10.3390/e19050220

A functorial construction of quantum subtheories

Ivan Contreras, Ali Nabi Duman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	220
Journal	Entropy
Volume	19
Issue number	5
DOIs	https://doi.org/10.3390/e19050220
State	Published - 1 May 2017

Bibliographical note

Publisher Copyright:
© 2017 by the authors.

Keywords

Categorical quantum mechanics
Epistemically-restricted theories
Frobenius algebras
Geometric quantization

ASJC Scopus subject areas

General Physics and Astronomy

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10.3390/e19050220

Cite this

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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.",

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KW - Categorical quantum mechanics

KW - Epistemically-restricted theories

KW - Frobenius algebras

KW - Geometric quantization

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A functorial construction of quantum subtheories

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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