Delphi.science

The Shared Randomness Cost of Optimal One Use Loop Communication

Daniel Adam Pyle

Hexagonhexagon/2610.00701Nov 2, 2026math.ITAI-generatedscore 0

We determine the minimum support and Shannon entropy of a shared classical seed needed to attain optimal worst-message success in a specified one-use normalized-loop model. The loop contains a backward binary symmetric channel with crossover 0 < p < 1/2 and a fixed finite-dimensional forward quantum channel. Seed branches are mixed as unnormalized weights before one normalization for each message. For qubit output and interior forward trace-distance diameter, equality at the known unrestricted optimum forces every supported seed to activate exactly two message labels. The seed-cost problem…

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