Non-signalling boxes and Bohrification

TL;DR

This paper explores how Bohrification provides a natural interpretative framework for non-signalling theories, specifically analyzing non-signalling box-worlds and their states within a topos-theoretic setting.

Contribution

It demonstrates that non-signalling box-world states correspond exactly to internal probability valuations in a Kripke topos, linking non-signalling theories with Bohrification.

Findings

Non-signalling box-world states are internal probability valuations.

Bohrification offers a natural interpretation for non-signalling theories.

The framework connects super-quantum correlations with topos-theoretic structures.

Abstract

The premise of this note is the following observation: the formalism of Bohrification is a natural place for the interpretation of general non-signalling theories. We demonstrate it through an analysis of so-called box-worlds, a popular framework for the discussion of systems exhibiting super-quantum correlations. In particular, we show that non-signalling box-world states are precisely the internal probability valuations on an internal frame in a Kripke topos naturally associated with a given box world.