Manuscript Em03-H@8 · Em03-H-v8.tex · section · 91e9e3bd

Packet, excitation code, and controls

Restricted continuum experiment › Packet, excitation code, and controls · lines 1139–1190

Em03-H@8#eq:primary

Set

f (ω) = 2 e^{- ω}, O_{j} = a_{j} (f), N_{g} = j \sum O_{j}^{†} O_{j},

ϕ (E) = 1_{[1, 2]} (E) / ρ_{C} (E),

γ_{0} = ϕ \otimes ∣ vac ⟩, γ_{1} = ϕ \otimes a_{1}^{†} (f) a_{2}^{†} (f) ∣ vac ⟩ .

Creation is linear and annihilation antilinear in its packet. These are normalized orthogonal even excitation states, not identified black-hole microstates. Packet operators are bounded CAR operators; they are not unsmeared coincident fields.

Direct integration gives

∥ f ∥ = 1, ⟨ f, h f ⟩ = 1/2, ⟨ f, h^{2} f ⟩ = 1/2.

The code-state storage-energy means are $3/2, 5/2$ , with variances $1/12, 7/12$ . They are not energy eigenvectors.

Extraction retains storage and adds

N_{R} + v N_{g} + w I + κ G_{g}, G_{g} = j \sum (O_{j}^{†} b_{j} + b_{j}^{†} O_{j}) .

The primary experiment remains

t_{0} = T = Ω = 1, v = 1, w = 0,

with pulse (eq:pulse). Other six species and bath modes remain vacuum.

Storage changes the occupied packet to $f_{st} (ω) = e^{- i ω t_{0}} f (ω)$ . Extraction still couples to the fixed $f$ . The common Schwarzian state evolves to $e^{- i (t_{0} + T) E} ϕ (E)$ . It remains factorized and independent of the logical input, so it is a harmless spectator for the reduced channel, while retained as a pure complementary factor.

Displayed formulas in this passage

Em03-H@8#eq:primary · line 1175
$t_{0} = T = Ω = 1, v = 1, w = 0,$
unlabeled · line 1142
$f (ω) = 2 e^{- ω}, O_{j} = a_{j} (f), N_{g} = j \sum O_{j}^{†} O_{j},$
unlabeled · line 1147
$ϕ (E) = 1_{[1, 2]} (E) / ρ_{C} (E),$
unlabeled · line 1150
$γ_{0} = ϕ \otimes ∣ vac ⟩, γ_{1} = ϕ \otimes a_{1}^{†} (f) a_{2}^{†} (f) ∣ vac ⟩ .$
unlabeled · line 1161
$∥ f ∥ = 1, ⟨ f, h f ⟩ = 1/2, ⟨ f, h^{2} f ⟩ = 1/2.$
unlabeled · line 1169
$N_{R} + v N_{g} + w I + κ G_{g}, G_{g} = j \sum (O_{j}^{†} b_{j} + b_{j}^{†} O_{j}) .$