Manuscript Hawk04-A@1 · Hawk04-A.tex · proposition · 526092ba

Proposition: Uniformly featureless radiation is incompatible with good recovery

Quantitative channel certificates › A quantitative incompatibility · lines 952–978 · proof included or linked

Hawk04-A@1#prop:thermal

If $N_{rep}$ is a replacement channel and

d_{⋄} (N, N_{rep}) \leq η,

then

ε_{rec} (N) \geq max {0, a_{d} - η} .

For finite-dimensional complete outputs,

a_{d} \leq η + 2 δ_{full} .

Proof. For every decoder, postprocessing contraction gives

d_{⋄} (DN, id_{C}) \geq d_{⋄} (D N_{rep}, id_{C}) - η .

The decoded replacement is constant, so Lemma lem:replacement gives the lower bound. Combine it with (eq:KSW).

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