Measurable No-signalling Correlations

TL;DR

This paper develops a framework for analyzing no-signalling correlations over complex spaces, introducing measurable versions of key theorems and linking non-local game values to measurable correlation classes.

Contribution

It defines measurable subclasses of no-signalling correlations and establishes measurable Stinespring's Dilation Theorem, connecting finite non-local game values to measurable correlation classes.

Findings

Defined local, quantum spatial, and quantum commuting measurable no-signalling correlations.

Established measurable versions of Stinespring's Dilation Theorem.

Connected asymptotic non-local game values to inner values of measurable games.

Abstract

We study no-signalling correlations, defined over a quadruple of second countable compact Hausdorff spaces. Using operator-valued information channels over abstract alphabets, we define the subclasses of local, quantum spatial and quantum commuting measurable no-signalling correlations. En route, we establish measurable versions of the Stinespring's Dilation Theorem. We define values of measurable non-local games of local, quantum spatial and quantum commuting type, as well as inner versions thereof, and show how the asymptotic values of a finite non-local game can be viewed as special cases of the corresponding inner values of a measurable game, canonically associated with the given finite game.