Manuscript Hawk06-A@1 · Hawk06-A.tex · section · c59fe67c

A specified deterministic decoder

A specified deterministic decoder · lines 793–821

We choose a finite optimization-defined decoder, not an unproved Petz estimate.

For a linear map $Φ$ , use the unnormalized Choi operator

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

Then $J_{n} (Φ) = J (Φ) / d$ for a diary-input channel.

At cut $k$ , let $A = A_{k}$ , $a_{A} = dim A = r_{k} h$ , and let $C_{D}$ be a decoder Choi variable on $A^{'} \otimes L_{out}$ . It defines

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

Set

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

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