Manuscript Hawk04-C@1 · Hawk04-C-v1.tex · corollary · 94d46352

Corollary: Near-constant accessible output is a lower certificate

Row 6: thermality, classical records, and information loss › A useful calibration: a constant accessible channel · lines 1357–1374 · proof included or linked

Hawk04-C@1#cor:featureless, Hawk04-C@1#eq:featureless-lower

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If $d_{⋄} (N, T_{ω}) \leq η$ , then

ε_{rec} (N) \geq max {0, q_{d} - η} .

Proof. For every decoder, contraction under postprocessing gives $d_{⋄} (DN, D T_{ω}) \leq η$ . The latter decoded comparison channel is a replacement. Lemma lem:constant and the triangle inequality give $d_{⋄} (DN, id_{C}) \geq q_{d} - η$ . Take the infimum.

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Hawk04-C@1#eq:featureless-lower · line 1360
$ε_{rec} (N) \geq max {0, q_{d} - η} .$

Nearby in this section

lemma: Lemma: Optimal recovery from a replacement channel
section: A useful calibration: a constant accessible channel