Manuscript X-D-ST@1 · X-D-ST.tex · section · e0cf8fdb

A specific complete-channel limit for the table

Finite Enter encoding of supplied limiting evaluations › A specific complete-channel limit for the table · lines 2242–2264

Choose one fixed scale $B_{tab} > 0$ large enough that the finitely many reports

v_{k, ε} = a_{i (k), ε} / B_{tab}, v_{k, 0} = a_{i (k), 0} / B_{tab}

lie in $[- 1, 1]$ for all sufficiently small widths. The dictionary and scale are installed data.

For $y = \pm 1$ , set

p_{y} (v) = \frac{1 + y v}{2},

and define

I_{v} (X) = k, y \sum ∣ k, y ⟩ ⟨ k, y ∣_{R} \otimes p_{y} (v_{k}) D_{k} X D_{k}^{†} .

Displayed formulas in this passage

unlabeled · line 2246
$v_{k, ε} = a_{i (k), ε} / B_{tab}, v_{k, 0} = a_{i (k), 0} / B_{tab}$
unlabeled · line 2255
$p_{y} (v) = \frac{1 + y v}{2},$
unlabeled · line 2259
$I_{v} (X) = k, y \sum ∣ k, y ⟩ ⟨ k, y ∣_{R} \otimes p_{y} (v_{k}) D_{k} X D_{k}^{†} .$