Stephanie Wehner

Consider two parties who want to agree on a common frequency band for communication in the presence of independent jammers. Such jammers block a different subset of bands at each site, where each party can observe only its own set of unjammed bands. Yet, they must agree on a common band without communicating. We first establish the optimal classical strategy, maximizing the probability they output a common frequency band in a single shot. We proceed to show that sharing an entangled pair of local dimension d allows the parties to coordinate strictly better, provided both the number of safe bands d and the spectrum size n are sufficiently large. We study explicit quantum strategies offering a pathway to near-term demonstrations, including an explicit strategy for d = 2 that outperforms the classical optimum for all spectrum sizes, achieving a 5.4% advantage asymptotically (in n) with just one shared Bell pair. Our approach is based on a general framework for constructing quantum strategies from classical spreading sequences via symmetric orthonormalization that may be of independent interest, and opens the door to concrete applications of quantum networks for cognitive radio and spread-spectrum communication.