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Mathematics > Category Theory

arXiv:1210.0615v1 (math)
[Submitted on 2 Oct 2012]

Title:The Born rule as structure of spectral bundles (extended abstract)

Authors:Bertfried Fauser, Guillaume Raynaud, Steven Vickers (School of Computer Science, University of Birmingham)
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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.
Comments: In Proceedings QPL 2011, arXiv:1210.0298
Subjects: Category Theory (math.CT); Quantum Physics (quant-ph)
ACM classes: F.0
Cite as: arXiv:1210.0615 [math.CT]
  (or arXiv:1210.0615v1 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.1210.0615
Journal reference: EPTCS 95, 2012, pp. 81-90
Related DOI: https://doi.org/10.4204/EPTCS.95.8

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 2 Oct 2012 00:34:35 UTC (20 KB)
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