# Optimal non-signalling violations via tensor norms

## TL;DR

This paper characterizes bipartite non-signalling distributions using tensor norms, providing bounds on Bell inequality violations that are close to quantum limits, thus deepening understanding of non-local correlations.

## Contribution

It introduces a tensor norm framework to precisely characterize non-signalling distributions and derives bounds on Bell violations, connecting non-signalling and quantum correlations.

## Key findings

- Non-signalling Bell violations are bounded close to quantum violations.
- Tensor norms effectively characterize non-signalling distributions.
- Upper bounds on violations are optimal and tight.

## Abstract

In this paper we characterize the set of bipartite non-signalling probability distributions in terms of tensor norms. Using this characterization we give optimal upper and lower bounds on Bell inequality violations when non-signalling distributions are considered. Interestingly, our upper bounds show that non-signalling Bell inequality violations cannot be significantly larger than quantum Bell inequality violations.