Manuscript Hawk05-A@1 · Hawk05-A.tex · remark · 449f85bb

Remark: Recovery is not raw-output purity

Complete preservation and the constant-complement criterion · lines 482–491

Hawk05-A@1#rem:purity

For a pure logical input, (eq:normalform) gives

S (N (∣ ψ ⟩ ⟨ ψ ∣)) = S (σ_{K}) .

Thus exact recovery can coexist with positive raw radiation entropy. The decoded logical output is pure; the accessible syndrome need not be. A pure fixed complement is the special case $r = 1$ .

Displayed formulas in this passage

unlabeled · line 485
$S (N (∣ ψ ⟩ ⟨ ψ ∣)) = S (σ_{K}) .$

Nearby in this section

theorem: Theorem: Complete isometric preservation
section: Complete preservation and the constant-complement criterion
theorem: Theorem: Exact whole-code recovery
corollary: Corollary: No-hiding, no duplicate whole-code recovery, and rank
section: Complete preservation and the constant-complement criterion
example: Example: Residual size is not a replacement estimate