Manuscript En07-B@1 · En07-B.tex · proposition · 45dff4a1

Proposition: More information-theoretic access cannot worsen unrestricted recovery

Featureless output, entropy, and availability · lines 882–897 · proof included or linked

En07-B@1#prop:availability

If $N_{s} = P_{t \to s} \circ N_{t}$ for a CPTP restriction $P_{t \to s}$ , then

ε_{rec} (N_{t}) \leq ε_{rec} (N_{s}) .

Proof. For any decoder $D_{s}$ , the channel $D_{t} = D_{s} P_{t \to s}$ is an admissible decoder for $N_{t}$ and has exactly the same decoded code channel. Take the infimum over $D_{s}$ .

Displayed formulas in this passage

unlabeled · line 887
$ε_{rec} (N_{t}) \leq ε_{rec} (N_{s}) .$

Nearby in this section

proposition: Proposition: Featureless accessible output obstructs recovery
remark: Remark: No temperature is encoded in the hypothesis
proposition: Proposition: Selected output entropy does not identify recovery
section: Featureless output, entropy, and availability
section: Featureless output, entropy, and availability