The Born Rule as Structure of Spectral Bundles

Bertfried Fauser; Guillaume Raynaud; Steven Vickers

doi:10.4204/EPTCS.95.8

The Born Rule as Structure of Spectral Bundles

Bertfried Fauser, Guillaume Raynaud, Steven Vickers

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Abstract

Topos approaches to quantum foundations are described in a unified way by means of spectral bundles, where the base space is a space of contexts and each fibre is its spectrum. Differences in variance are due to the bundle being a fibration or opfibration. Relative to this structure, the probabilistic predictions of the Born rule in finite dimensional settings are then described as a section of a bundle of valuations. The construction uses in an essential way the geometric nature of the valuation locale monad.

Original language	English
Title of host publication	Proceedings of the 8th International Workshop on Quantum Physics and Logic, Nijmegen 2011
Editors	Bart Jacobs, Peter Selinger, Bas Spitters
Pages	81-90
Number of pages	10
Volume	95
DOIs	https://doi.org/10.4204/EPTCS.95.8
Publication status	Published - 2012

Publication series

Name	EPTCS
Volume	95
ISSN (Electronic)	2075-2180

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10.4204/EPTCS.95.8

Fauser_et_al_Born_Rule_Electronic_Proceedings_in_Theoretical_Computer_Science_2012
Checked May 2015
Final published version, 110 KBLicence: Unspecified

Applications of geometric logic to topos approaches to quantum theory
Vickers, S. (Principal Investigator)
Engineering & Physical Science Research Council
1/09/09 → 31/08/12
Project: Research Councils

Cite this

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The Born Rule as Structure of Spectral Bundles. / Fauser, Bertfried; Raynaud, Guillaume; Vickers, Steven.
Proceedings of the 8th International Workshop on Quantum Physics and Logic, Nijmegen 2011. ed. / Bart Jacobs; Peter Selinger; Bas Spitters. Vol. 95 2012. p. 81-90 (EPTCS; Vol. 95).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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The Born Rule as Structure of Spectral Bundles

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Applications of geometric logic to topos approaches to quantum theory

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