Manuscript En02-D@4 · En02-D-v4.tex · section · e19ec871

Analytical transport controls and horizon-dependent execution

Analytical transport controls and horizon-dependent execution · lines 984–1004

Use stage A, identity inter-emission gates, transmission $γ$ , and initialization

J_{loc} ∣ ψ ⟩ = ∣ 0 ⟩^{\otimes (K - 1)} ∣ ψ ⟩ .

An initial sequence of $ℓ$ adjacent swaps moves the message to extraction position $d = K - ℓ$ . Its mode is $n_{*} = K - d + 1$ . This is transport, not scrambling.

Let $T_{d}$ be its emission time, $a_{t} = Pr (T_{d} \leq t)$ , $b_{t} = Pr (T_{d} = t)$ . The population recursion gives

a_{t} = n = 0 \sum^{K - d} π_{t} (n), b_{t} = r_{K - d + 1} π_{t - 1} (K - d + 1) .

Displayed formulas in this passage

unlabeled · line 989
$J_{loc} ∣ ψ ⟩ = ∣ 0 ⟩^{\otimes (K - 1)} ∣ ψ ⟩ .$
unlabeled · line 1000
$a_{t} = n = 0 \sum^{K - d} π_{t} (n), b_{t} = r_{K - d + 1} π_{t - 1} (K - d + 1) .$

Nearby in this section

proposition: Proposition: Transport controls
section: Analytical transport controls and horizon-dependent execution