Manuscript Hawk05-A@1 · Hawk05-A.tex · lemma · 449f85bb

Lemma: Complete readout dilation

Destructive Enter, hybrid recovery, and readout-and-drop › The destructive instrument and its complete dilation · lines 691–711 · proof included or linked

Hawk05-A@1#lem:readoutdilation

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An isometric dilation of destructive basis readout is

W_{M} ∣ y ⟩_{M} = ∣ y ⟩_{Y} ∣ y ⟩_{L},

where $L$ is unreturned. For a superposition,

W_{M} y \sum α_{y} ∣ y ⟩ = y \sum α_{y} ∣ y ⟩_{Y} ∣ y ⟩_{L} .

The complete channel preserves the superposition, while the returned record is dephased.

Proof. The columns of $W_{M}$ are orthonormal. Tracing $L$ gives (eq:enter) without $K$ ; tensoring with $K$ gives the general statement.

Displayed formulas in this passage

unlabeled · line 694
$W_{M} ∣ y ⟩_{M} = ∣ y ⟩_{Y} ∣ y ⟩_{L},$
unlabeled · line 698
$W_{M} y \sum α_{y} ∣ y ⟩ = y \sum α_{y} ∣ y ⟩_{Y} ∣ y ⟩_{L} .$

Nearby in this section

section: The destructive instrument and its complete dilation
section: The destructive instrument and its complete dilation
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section: The destructive instrument and its complete dilation