Manuscript En06-B@1 · En06-B.tex · section · ee886ae8

Operational–algebraic compatibility

Operational–algebraic compatibility · lines 1897–1920

En06-B@1#eq:reporteffects

For any logical input state $ρ$ , let

σ_{ρ} = ρ \otimes ∣ 0 ⟩ ⟨ 0 ∣_{R_{L} E_{L} F_{L} R_{R} E_{R} F_{R}}^{\otimes 6}

on $H_{0}$ , and define

ω_{ρ} (A) = Tr (σ_{ρ} A) .

Let $Π_{a}^{R_{L}}$ and $Π_{b}^{R_{R}}$ be the output record projections, and set

M_{ab} = U^{†} (Π_{a}^{R_{L}} Π_{b}^{R_{R}}) U .

Identities on all omitted factors are understood.

Displayed formulas in this passage

unlabeled · line 1900
$σ_{ρ} = ρ \otimes ∣ 0 ⟩ ⟨ 0 ∣_{R_{L} E_{L} F_{L} R_{R} E_{R} F_{R}}^{\otimes 6}$
unlabeled · line 1906
$ω_{ρ} (A) = Tr (σ_{ρ} A) .$
En06-B@1#eq:reporteffects · line 1912
$M_{ab} = U^{†} (Π_{a}^{R_{L}} Π_{b}^{R_{R}}) U .$