2012/10/02 by Bertfried Fauser, Guillaume Raynaud, Steven Vickers
Mathematics · Physics and Astronomy · #math.CT #quant-ph
paper · pdf · doi:10.4204/eptcs.95.8
published as EPTCS 95, 2012, pp. 81-90 · In Proceedings QPL 2011, arXiv:1210.0298
arxiv created 2012/10/02 · arxiv updated 2012/10/03
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.