Manuscript Oai069-A@1 · Oai069-A.tex · section · a4913aab

Access dependence, named effects, and sharp exclusions

Access dependence, named effects, and sharp exclusions · lines 883–905

Oai069-A@1#eq:one-leg

Let $N_{1}$ retain $J, R_{1}$ but discard $R_{2}, B$ . For a fixed sector,

N_{1, k} (ρ) = Δ_{Z} (H Z^{ϵ_{k}} (Tr_{K} ρ) Z^{ϵ_{k}} H),

where

Δ_{P} (σ) = \frac{1}{2} (σ + P σ P) .

Applying $Z^{ϵ_{k}} H$ to $R_{1}$ gives the complete decoded channel

D_{1} N_{1} = label return \otimes Δ_{X} \circ Tr_{K} .

The same description holds for $R_{2}$ alone, with the appropriate identification of that receiver leg.

Displayed formulas in this passage

Oai069-A@1#eq:one-leg · line 898
$D_{1} N_{1} = label return \otimes Δ_{X} \circ Tr_{K} .$
unlabeled · line 887
$N_{1, k} (ρ) = Δ_{Z} (H Z^{ϵ_{k}} (Tr_{K} ρ) Z^{ϵ_{k}} H),$
unlabeled · line 893
$Δ_{P} (σ) = \frac{1}{2} (σ + P σ P) .$