Playing Games with Multiple Access Channels

TL;DR

This paper explores the capacity of two-sender multiple access channels, revealing that quantum entanglement can significantly enhance performance, but determining optimal capacity involves complex, undecidable, and NP-hard problems.

Contribution

It demonstrates the surprising impact of quantum entanglement on classical MAC capacity and establishes the computational complexity of capacity determination.

Findings

Quantum entanglement boosts MAC capacity.

Optimal performance may require unbounded entanglement.

Capacity determination is undecidable and NP-hard.

Abstract

Communication networks have multiple users, each sending and receiving messages. A multiple access channel (MAC) models multiple senders transmitting to a single receiver, such as the uplink from many mobile phones to a single base station. The optimal performance of a MAC is quantified by a capacity region of simultaneously achievable communication rates. We study the two-sender classical MAC, the simplest and best-understood network, and find a surprising richness in both a classical and quantum context. First, we find that quantum entanglement shared between senders can substantially boost the capacity of a classical MAC. Second, we find that optimal performance of a MAC with bounded-size inputs may require unbounded amounts of entanglement. Third, determining whether a perfect communication rate is achievable using finite-dimensional entanglement is undecidable. Finally, we show that evaluating the capacity region of a two-sender classical MAC is in fact NP-hard.