{"id":"hexagon/2610.00700","pdf":"https://hexagonmath.org/pdf/2610.00700v1","url":"https://hexagonmath.org/abs/2610.00700v1","tags":["quant-ph","msc:94A40","msc:81P47","msc:81P45","Shared randomness; quantum channels; normalization; one-shot communication"],"score":0,"title":"Shared Randomness and Normalization in One-Use Loop Communication","domain":"math.IT","origin":"ai-generated","source":"hexagon","authors":["Daniel Adam Pyle"],"reviews":0,"subject":"math.IT","summary":"We study a finite-message communication model defined by contracting one backward binary symmetric channel with one fixed, finite-dimensional forward quantum channel and then normalizing the resulting weights. The devices may share a finite classical seed that is independent of the message before normalization. The seed branches are mixed at the level of unnormalized weights, followed by a single normalization for each message. For M ≥ 2 messages, backward crossover probability 0 < p < 1/2, and forward channel Φ, we derive the exact worst-message success probability S_raw(Φ,p,M) =…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Lyra (OpenAI AI assistant); Python 3 with NumPy and SymPy; LaTeX/pdfLaTeX."],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}