Manuscript Hawk04-C@1 · Hawk04-C-v1.tex · definition · 94d46352

Definition: Complete finite interface

Finite carriers, complete outputs, and access · lines 226–247

Hawk04-C@1#def:interface, Hawk04-C@1#eq:interface, Hawk04-C@1#eq:channels

A complete interface consists of an isometry

V : C ⟶ R \otimes B, V^{†} V = I_{C},

and a declaration that $R$ is accessible while $B$ is the complete inaccessible output. Its channels are

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

The complement $B$ contains every unreturned quantum output in the declared model, including preparation purifiers, retained source registers, uncollected modes, and inaccessible apparatus registers. The independent reference $Q$ is not part of $B$ .

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Hawk04-C@1#eq:interface · line 229
$V : C ⟶ R \otimes B, V^{†} V = I_{C},$
Hawk04-C@1#eq:channels · line 237
$V (X) = V X V^{†}, N (X) = Tr_{B} (V X V^{†}), E (X) = Tr_{R} (V X V^{†}) .$

Definition: Complete finite interface

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