Manuscript Oai212-A@1 · Oai212-A.tex · section · 79323841

A declared complete-channel lift

Bridge 1: an exact controlled operator-spreading model › A declared complete-channel lift · lines 634–647

A classical process and a quantum channel have different codomains. To state a complete-channel comparison, define the target lift

Ψ_{G, t} (ρ) = E_{τ} [∣ r (τ, t)⟩ ⟨ r (τ, t) ∣ \otimes U_{τ} (t) ρ U_{τ} (t)^{†}],

where $r$ is the finite flag-and-parent record. All payload qubits are returned. This target is specified before any approximation.

Displayed formulas in this passage

unlabeled · line 638
$Ψ_{G, t} (ρ) = E_{τ} [∣ r (τ, t)⟩ ⟨ r (τ, t) ∣ \otimes U_{τ} (t) ρ U_{τ} (t)^{†}],$