Manuscript Hawk07-A@1 · Hawk07-A.tex · section · f9c0f5da

A deterministic finite prescription

One specified decoder core › A deterministic finite prescription · lines 912–934

For a map $Φ$ , use the unnormalized input-first Choi operator

J (Φ) = i, j \sum ∣ i ⟩ ⟨ j ∣ \otimes Φ (∣ i ⟩ ⟨ j ∣) .

At $k_{*}$ , let $R = R_{k_{*}}$ , $q_{R} = dim R$ . A decoder Choi matrix $C_{D}$ on $R^{'} \otimes L_{out}$ defines

D_{C} (Y) = Tr_{R^{'}} [(Y^{T} \otimes I_{L}) C_{D}] .

Set

J_{Δ} (C) = J (D_{C} N_{k_{*}}^{U} - id_{L}) .

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