Randomness compression in communication networks

TL;DR

This paper introduces a new upper bound on the shared randomness needed to approximate correlations in communication networks, showing potential resource savings when small errors are acceptable.

Contribution

It develops a novel approximation bound for arbitrary networks that outperforms existing bounds for exact distributions, highlighting efficiency gains.

Findings

Significant resource savings possible with approximate distributions

New upper bound outperforms previous bounds in certain scenarios

Applicable to common network scenarios like Bell and triangle scenarios

Abstract

Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks and showcase instances where it significantly outperforms the best-known upper bounds for the exact case. This demonstrates that one can have substantial savings in resources if small perturbations are acceptable. We derive our bound using Hoeffding's inequality and apply it to various commonly-used communication networks such as the Bell scenario and triangle scenario.