Proposition: Identical sector record, opposite recovery

Fix any record $\mathcal{R}$ and a logical dimension $d\ge 2$. There are independent completions with the same $d$-dimensional accessible and complementary spaces whose optimal full-code recovery errors are $0$ and $1-d^{-2}$. For every pure code input, accessible entropy is zero in both.

Proof. Take $R=B=C={\mathbb{C}}^d$, and set

The first accessible channel is identity. The second is replacement, and every decoder after it is again replacement.

For the normalized Bell input, any replacement output has Bell overlap $d^{-2}$. Testing the Bell projector gives recovery error at least $1-d^{-2}$. Returning $I_C/d$ attains this bound: the depolarizing channel is the average of $d^2$ Weyl conjugations; separating the identity term and using the triangle inequality gives the upper bound $1-d^{-2}$.

Pure inputs give pure accessible outputs in both completions. Neither construction changes any part of $\mathcal{R}$.