Manuscript Em05-B@1 · Em05-B-v1.tex · corollary · 6c050f5b

Corollary: Exact recovery endpoint

Exact recovery and complementary leakage › The constant-complement criterion · lines 813–827 · proof included or linked

Em05-B@1#cor:exactEndpoint

The extractor admits exact CPTP recovery if and only if $η = 1$ .

Proof. For $t > 0$ ,

A_{11}^{†} A_{11} = t^{2} ∣1 ⟩ ⟨ 1∣

is not scalar. Equivalently, the complementary basis outputs are unequal by (eq:rhoE). At $η = 1$ , the complement is vacuum replacement and the accessible map is an isometric encoding.

Displayed formulas in this passage

unlabeled · line 820
$A_{11}^{†} A_{11} = t^{2} ∣1 ⟩ ⟨ 1∣$

Nearby in this section

section: The constant-complement criterion
theorem: Theorem: Exact recovery if and only if the complement is constant