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

Terminal discard, reset, and nongeometric costs

Terminal discard, reset, and nongeometric costs · lines 1688–1704

An appended residual album obeys (eq:album), but need not describe the payload. Nothing in this proposition moves the payload back out of the receiver or turns a classical album into its decoder.

If the complete terminal operation is an isometry $W_{B} : B \to B^{'}$ , then

C^{'} = Ad_{W_{B}} C, δ_{full} (C^{'}) = δ_{full} (C) .

The forward inequality is contraction. A CPTP left inverse of the isometric channel gives the reverse inequality. The residual may leave the returned address space while remaining in the complete physical output CheungEn07A,CheungHawk07A.

Displayed formulas in this passage

unlabeled · line 1696
$C^{'} = Ad_{W_{B}} C, δ_{full} (C^{'}) = δ_{full} (C) .$

Nearby in this section

proposition: Proposition: Residual readout does not retract the return