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

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.

In Proceedings QPL 2011, arXiv:1210.0298

References in corpus (4)

• A topos for algebraic quantum theory
• Intuitionistic quantum logic of an n-level system
• Integrals and Valuations
• The space of measurement outcomes as a spectrum for non-commutative algebras

Cited by in corpus (1)

• A Topos Theory Foundation for Quantum Mechanics