Remarks on CHSH inequality, Tsirelson bound, Popescu-Rohlich boxes and inner product spaces

TL;DR

This paper discusses the mathematical foundations of quantum correlations, providing a simple proof of the Tsirelson bound, and explores their relation to Popescu-Rohrlich boxes and indefinite inner product spaces.

Contribution

It offers a straightforward proof of the Tsirelson bound and examines the connections between quantum correlations, PR boxes, and indefinite inner product spaces.

Findings

Proof of Tsirelson bound based on correlation matrix extension

Relation between EPR correlations and Hilbert space models

Discussion of PR boxes and indefinite inner product spaces

Abstract

The EPR correlation matrix admit a Hilbert model if it can be extended to a positive full correlation matrix. A simple proof of the corresponding Tsirelson bound is given and the relations to PR boxes and indefinite inner product spaces are briefly discussed.