The space of measurement outcomes as a spectrum for non-commutative algebras

Abstract

Bohrification defines a locale of hidden variables internal in a topos. We find that externally this is the space of partial measurement outcomes. By considering the double negation sheafification, we obtain the space of measurement outcomes which coincides with the spectrum for commutative C*-algebras.

References in corpus (1)

• Intuitionistic quantum logic of an n-level system

Cited by in corpus (2)

• The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach
• The Born rule as structure of spectral bundles (extended abstract)