Super - quantum and quantum enhancements of two - sender channels

This thesis studies the consequences of 'super-quantum non-local correlations', which are hypothetical violations of Bell/CHSH inequalities that are stronger more nonlocal than quantum mechanics allows, yet weak enough to respect special relativity in prohibiting faster-than-light communication. Understanding the power of such correlations will yield insight into the non-locality of quantum mechanics. Whereas previous studies of super-quantum correlations have demonstrated enhancements in cryptography and computation of distributed functions, this work opens up a new direction of research by showing that they can also enhance the capacity of classical communication over a noisy channel. Our results exhibit a trifecta of proof-of-concept channels: first, we show an interference channel between two sender-receiver pairs where the senders are not allowed to communicate, for which a shared super-quantum bit allows perfect classical communication. This feat is not achievable with the best classical (senders share no resources) or quantum-assisted (senders share entanglement) strategies. We next show two examples that are conjectured to demonstrate the following capacity separations: an interference channel that strictly separates super-quantum from quantum-assisted strategies, and quantum-assisted from classical strategies; and, lastly, a multiple-access channel that strictly separates superquantum-assisted strategies from classical ones. At the heart of some of these examples is a novel connection between multi-sender channels and multi-player XOR and pseudo-telepathy games. Thesis Supervisor: Peter W. Shor Title: Henry Adams Morss Jr. Professor of Applied Mathematics