Manuscript En07-C@1 · En07-C.tex · definition · 3f7e9ebb

Definition: Complete finite code interface

The complete finite interface and error conventions · lines 246–266

En07-C@1#def:interface, En07-C@1#eq:interface, En07-C@1#eq:channels

Let $C, R, B$ be finite-dimensional Hilbert spaces, with $d = dim C \geq 2$ . A complete code interface is an isometry

V : C ⟶ R \otimes B, V^{†} V = I_{C} .

Its complete, accessible, and complementary channels are

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

The factor $R$ is the declared quantum access. The factor $B$ contains every other output of the complete prepared dilation, including preparation purifiers, apparatus environments, lost carriers, and retained memories.

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En07-C@1#eq:interface · line 250
$V : C ⟶ R \otimes B, V^{†} V = I_{C} .$
En07-C@1#eq:channels · line 256
$V (X) = V X V^{†}, N (X) = Tr_{B} (V X V^{†}), E (X) = Tr_{R} (V X V^{†}) .$

Definition: Complete finite code interface

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