Manuscript En01-A@1 · En01-A.tex · definition · 558b972b

Definition: Cross operators and visibility

Cross operators, fidelity, screening, and noisy architecture · lines 1257–1272

En01-A@1#def:visibility, En01-A@1#eq:cross-expansion

For supported $r \neq = r^{'}$ , set

Γ^{S}_{r r^{'}} = tr_{S} ∣ Φ_{r} ⟩ ⟨ Φ_{r^{'}} ∣, v_{r r^{'}} (S) = ∥ Γ^{S}_{r r^{'}} ∥_{1} .

Then

tr_{S} X_{J} = r < r^{'} J -split \sum p_{r} p_{r^{'}} (Γ^{S}_{r r^{'}} + Γ^{S †}_{r r^{'}}) .

Displayed formulas in this passage

En01-A@1#eq:cross-expansion · line 1265
$tr_{S} X_{J} = r < r^{'} J -split \sum p_{r} p_{r^{'}} (Γ^{S}_{r r^{'}} + Γ^{S †}_{r r^{'}}) .$
unlabeled · line 1259
$Γ^{S}_{r r^{'}} = tr_{S} ∣ Φ_{r} ⟩ ⟨ Φ_{r^{'}} ∣, v_{r r^{'}} (S) = ∥ Γ^{S}_{r r^{'}} ∥_{1} .$