Manuscript Oai280-B@1 · Oai280-B.tex · section · 6d92ab75

One unambiguous end-to-end channel

Access as a circuit invariant and the complete channel › One unambiguous end-to-end channel · lines 1080–1123

Oai280-B@1#eq:implemented

Let

V : B (C) \to B (H_{\partial})

be the implemented encoder channel, and let $E_{\partial}$ be the declared complete boundary process. Define

N_{0, A} Λ_{0, A} = Tr_{A ˉ} \circ E_{\partial} \circ V, = D_{A} \circ N_{0, A} .

Tensor permutations are understood as in (eq:accesschannels). Thus:

C V H_{\partial} E_{\partial} H_{A} \otimes H_{A ˉ} not received H_{A ˉ} Tr_{A ˉ} H_{A} received interface H_{A} D_{A} C_{out}

The independent reference $Q$ bypasses this entire channel and is used only in final validation.

For an after-loss process $E_{A}$ , the experiment is instead

D_{A} E_{A} Tr_{A ˉ} V .

This is a different ordering. Equality requires its own theorem and is not presumed.

Displayed formulas in this passage

Oai280-B@1#eq:implemented · line 1089
$N_{0, A} Λ_{0, A} = Tr_{A ˉ} \circ E_{\partial} \circ V, = D_{A} \circ N_{0, A} .$
unlabeled · line 1083
$V : B (C) \to B (H_{\partial})$
unlabeled · line 1101
$C V H_{\partial} E_{\partial} H_{A} \otimes H_{A ˉ} not received H_{A ˉ} Tr_{A ˉ} H_{A} received interface H_{A} D_{A} C_{out}$
unlabeled · line 1117
$D_{A} E_{A} Tr_{A ˉ} V .$