Shared Randomness and Normalization in One-Use Loop Communication
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) =…
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