Violating the Shannon capacity of metric graphs with entanglement.

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 D, Mančinska L, Matthews W, Ozols M, Roy A (2012) Commun Math Phys 311:97-111], two examples of graphs were presented whose Shannon capacity is strictly less than the capacity attainable if the sender and receiver have entangled quantum systems. Here, we give natural, possibly infinite, families of graphs for which the entanglement-assisted capacity exceeds the Shannon capacity.