Manuscript Oai069-A@1 · Oai069-A.tex · section · a4913aab

A dimension-explicit Choi bound

Complete coverage and simultaneous finite-confidence certification › A dimension-explicit Choi bound · lines 1073–1088

Oai069-A@1#eq:blockerror

The dimension factor is retained. A high average Choi overlap does not become a dimension-free worst-case recovery assertion.

If a direct-sum implementation is specified by its block channels, then

d_{⋄}_{\oplus} (Φ, T) = k max d_{⋄} (Φ_{k}, T_{k}) .

The upper bound follows by summing block trace distances weighted by block trace. The reverse bound is obtained by choosing one input block.

Displayed formulas in this passage

Oai069-A@1#eq:blockerror · line 1080
$d_{⋄}_{\oplus} (Φ, T) = k max d_{⋄} (Φ_{k}, T_{k}) .$