Manuscript Hawk07-B@1 · Hawk07-B.tex · definition · b9785538

Definition: Complete interface and diagnostics

Complete interfaces and their information tasks · lines 307–335

Hawk07-B@1#def:interface

A complete interface is an isometry

V : L ⟶ R \otimes B, dim L = d \geq 2.

Its accessible and complementary channels are

N (X) = Tr_{B} (V X V^{†}), C (X) = Tr_{R} (V X V^{†}) .

Every unreturned purifier, lost mode, apparatus environment, and record store required by the declared realization belongs to the complete residual. An untouched external reference is not granted to the decoder.

For a state $τ$ , define

T_{τ} (X) = Tr (X) τ,

ε_{rec} (N) = D CPTP in f d_{⋄} (DN, id_{L}), δ_{full} (C) = τ_{B} in f d_{⋄} (C, T_{τ_{B}}) .

Write $a_{d} = 1 - d^{- 2}$ and $b_{d} = 1 - d^{- 1}$ .

Displayed formulas in this passage

unlabeled · line 310
$V : L ⟶ R \otimes B, dim L = d \geq 2.$
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$N (X) = Tr_{B} (V X V^{†}), C (X) = Tr_{R} (V X V^{†}) .$
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$T_{τ} (X) = Tr (X) τ,$
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$ε_{rec} (N) = D CPTP in f d_{⋄} (DN, id_{L}), δ_{full} (C) = τ_{B} in f d_{⋄} (C, T_{τ_{B}}) .$

Definition: Complete interface and diagnostics

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