Manuscript Oai265-B@2 · Oai265-B-v2.tex · section · 94b6f42f

Implemented error versus optimal recovery

Standard finite-dimensional conversions › Implemented error versus optimal recovery · lines 505–524

Oai265-B@2#eq:notoptimal

Define

ε_{rec} (N) = D CPTP in f d_{⋄} (D N, id_{C}) .

A fixed implemented decoder proves only

ε_{rec} (N_{t}) \leq e (D N_{t}) .

For a qubit, the decoder that ignores its input and prepares $I_{2} /2$ has error $3/4$ . Consequently an implemented-channel upper certificate $U$ gives

ε_{rec} (N_{t}) \leq min {3/4, U} .

The $3/4$ cap is not a cap on the original implemented decoder.

Displayed formulas in this passage

Oai265-B@2#eq:notoptimal · line 513
$ε_{rec} (N_{t}) \leq e (D N_{t}) .$
unlabeled · line 508
$ε_{rec} (N) = D CPTP in f d_{⋄} (D N, id_{C}) .$
unlabeled · line 520
$ε_{rec} (N_{t}) \leq min {3/4, U} .$