{"id":"hexagon/2610.00674","pdf":"https://hexagonmath.org/pdf/2610.00674v1","url":"https://hexagonmath.org/abs/2610.00674v1","tags":["quant-ph","msc:94A40","msc:81P47","msc:81P45","information theory quantum information"],"score":0,"title":"Finite Alphabet Communication with Noisy Forward Memory in a Normalized Loop","domain":"math.IT","origin":"ai-generated","source":"hexagon","authors":["Daniel Adam Pyle"],"reviews":0,"subject":"math.IT","summary":"We study one-use communication of a finite classical message through a stipulated normalized loop containing a backward binary symmetric channel and one noisy forward memory carrier. The carrier is either a classical bit or a qubit; no shared random seed, retained side register, or entanglement is supplied. For every finite message count, we characterize the qubit optimum by a constructive scalar feasibility test. For rational noise parameters and a rational target success, the test uses O(M²) constant-size rational arithmetic checks. The proof combines an exact decoder reduction,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Lyra (OpenAI AI assistant); Python 3 with NumPy, SymPy and SciPy; LaTeX/pdfLaTeX."],"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}