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Manuscript Hawk05-A@1 · Hawk05-A.tex · proposition · 449f85bb

Proposition: Featureless accessible output is a lower bound

Replacement and classical-record benchmarks · lines 563–585 · proof included or linked

Hawk05-A@1#prop:featureless

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If

d_{⋄} (N, T_{τ_{A}}) \leq η,

then

ε_{rec} (N) \geq max {0, a_{d} - η} .

The replacement state may be pure or mixed.

Proof. For every decoder, contraction and the triangle inequality give

d_{⋄} (DN, id_{C}) \geq d_{⋄} (D T_{τ_{A}}, id_{C}) - η \geq a_{d} - η .

Take the infimum.

Displayed formulas in this passage

unlabeled · line 566
$d_{⋄} (N, T_{τ_{A}}) \leq η,$
unlabeled · line 570
$ε_{rec} (N) \geq max {0, a_{d} - η} .$
unlabeled · line 578
$d_{⋄} (DN, id_{C}) \geq d_{⋄} (D T_{τ_{A}}, id_{C}) - η \geq a_{d} - η .$

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