Manuscript Hawk05-C@1 · Hawk05-C.tex · section · ba0719f1

A deterministic Petz candidate and its certificate

Access algebras and independently certified recovery › A deterministic Petz candidate and its certificate · lines 1651–1671

Hawk05-C@1#eq:petz

Let $N : C \to R$ be a supplied finite proxy channel and choose a full-rank code state $σ_{C}$ . Set

s_{R} = N (σ_{C}), P = supp s_{R},

and use the inverse of $s_{R}$ only on its support. For a fixed code state $ω_{C}$ , define

R_{σ, N} (Y) = σ_{C}^{1/2} N^{*} (s_{R}^{- 1/2} P Y P s_{R}^{- 1/2}) σ_{C}^{1/2} + Tr ((I - P) Y) ω_{C} .

Displayed formulas in this passage

Hawk05-C@1#eq:petz · line 1662
$R_{σ, N} (Y) = σ_{C}^{1/2} N^{*} (s_{R}^{- 1/2} P Y P s_{R}^{- 1/2}) σ_{C}^{1/2} + Tr ((I - P) Y) ω_{C} .$
unlabeled · line 1656
$s_{R} = N (σ_{C}), P = supp s_{R},$