Violating the Shannon capacity of metric graphs with entanglement

TL;DR

This paper demonstrates that quantum entanglement can increase the capacity of certain graphs beyond the classical Shannon capacity, challenging traditional limits in information theory.

Contribution

The authors introduce new families of graphs where entangled quantum systems enable higher communication capacities than classical Shannon limits.

Findings

Entangled capacity exceeds Shannon capacity for certain graphs.

New families of graphs demonstrate quantum advantage in communication.

Results suggest quantum resources can fundamentally alter information limits.

Abstract

The Shannon capacity of a graph G is the maximum asymptotic rate at which messages can be sent with zero probability of error through a noisy channel with confusability graph G. This extensively studied graph parameter disregards the fact that on atomic scales, Nature behaves in line with quantum mechanics. Entanglement, arguably the most counterintuitive feature of the theory, turns out to be a useful resource for communication across noisy channels. Recently, Leung, Mancinska, Matthews, Ozols and Roy [Comm. Math. Phys. 311, 2012] presented two examples of graphs whose Shannon capacity is strictly less than the capacity attainable if the sender and receiver have entangled quantum systems. Here we give new, possibly infinite, families of graphs for which the entangled capacity exceeds the Shannon capacity.