Manuscript Hawk07-B@1 · Hawk07-B.tex · proposition · b9785538

Proposition: Purely classical return has a permanent floor

Hybrid communication and causal limitations · lines 1455–1472 · proof included or linked

Hawk07-B@1#prop:classical

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If the entire returned interface is classical, every deterministic decoder has

The full-diamond floor is .

Proof. A decoder of a classical channel is measure-and-prepare and hence entanglement breaking EntanglementBreaking. The Bell-input output is separable. A product vector has Bell squared overlap at most ; convexity gives the same bound for a separable state. Testing the Bell projector proves the claim.

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