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

Proposition: Transport controls

Analytical transport controls and horizon-dependent execution · lines 1005–1041 · proof included or linked

En02-D@4#prop:transport

Unrestricted recovery and a one-retained-qubit programme satisfy

ε_{IT} (t) = ε_{op} (q_{A} + 1, t) = \frac{3}{4} (1 - γ a_{t}) .

A $q_{A}$ -slot programme S0 implements

γ b_{t} id + γ (a_{t} - b_{t}) Δ_{Z} + (1 - γ a_{t}) T

and has achieved error

e_{S0} (t) = \frac{γ}{2} (a_{t} - b_{t}) + \frac{3}{4} (1 - γ a_{t}) .

No stochastic $q_{A}$ -slot optimum is asserted.

Proof. If the message mode is transmitted by the horizon, it carries the message exactly. Otherwise the message remains in a different core sector or a reflected message mode, and the accessible channel is constant. These success and failure subspaces are distinguished in the complement, so their cross terms vanish. Bell witnesses give the lower bound.

S1 retains the observed message rail through later arrivals. S0 measures an earlier-arriving message rail in $Z$ and consumes it, retaining a classical outcome. If the message arrives at the final opportunity, S0 returns it directly without a logical measurement. An earlier record causes eigenstate preparation after the last packet; no record causes preparation of $I /2$ . The stated complete channel follows.

Displayed formulas in this passage

unlabeled · line 1008
$ε_{IT} (t) = ε_{op} (q_{A} + 1, t) = \frac{3}{4} (1 - γ a_{t}) .$
unlabeled · line 1012
$γ b_{t} id + γ (a_{t} - b_{t}) Δ_{Z} + (1 - γ a_{t}) T$
unlabeled · line 1017
$e_{S0} (t) = \frac{γ}{2} (a_{t} - b_{t}) + \frac{3}{4} (1 - γ a_{t}) .$

Proposition: Transport controls

Displayed formulas in this passage

Nearby in this section