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arXiv · 1210.0615

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

Bertfried Fauser·Guillaume Raynaud·Steven Vickers
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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.

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Bertfried Fauser, Guillaume Raynaud, Steven Vickers. 2012-10-02. The Born rule as structure of spectral bundles (extended abstract). https://doi.org/10.4204/eptcs.95.8

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