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First page of Quantum Advantage for Coordinated Frequency Selection Against Distributed Jammers

Quantum Advantage for Coordinated Frequency Selection Against Distributed Jammers

Stephanie Wehner

quant-ph Apr 22, 2026 · v1
Proofs of the classical optimum and quantum advantage results were formalized in Lean 4, assisted by Aristotle and Claude Code, with code released.
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.

Two parties facing independent jammers each see only their own set of unjammed frequency bands. They must agree on a common band without communicating, and the question is whether shared entanglement improves their single-shot success probability over classical strategies.

The authors derive the optimal classical coordination strategy. They then build quantum strategies from classical spreading sequences via symmetric (Löwdin) orthonormalization on a shared maximally entangled state of local dimension d. Explicit constructions (simplex, harmonic, MUB, SIC, Alltop) are analyzed and compared numerically. The proofs were converted from LaTeX to Lean 4 with AI assistance and released alongside the numerical code.

Entanglement gives a strict advantage when both d and n are sufficiently large. An explicit d = 2 strategy beats the classical optimum for all spectrum sizes, with an asymptotic advantage of about 5.4% using one Bell pair.

ndω_clOpt. quantum
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Classical optimum vs. best quantum strategy (selected cases)