Manuscript Hawk04-B@2 · Hawk04-B.tex · section · ba3b0713

Destructive partial readout

A finite typed circuit semantics › Destructive partial readout · lines 668–698

Hawk04-B@2#eq:Enter

Let $S$ be $s$ measured qubits, and let $T$ be the surviving quantum register. Set

M_{x} = ⟨ x ∣_{S} \otimes I_{T}, x \in {0, 1}^{s} .

The observable instrument is

E_{S} (ρ) = x \sum ∣ x ⟩ ⟨ x ∣_{K} \otimes M_{x} ρ M_{x}^{†} .

The measured names in $S$ are consumed. The surviving quantum output is $T$ , not a renamed copy of $S$ .

For a pure input,

p_{x} = ∥ M_{x} ψ ∥^{2}, ψ_{x} = \frac{M _{x} ψ}{p _{x}} if p_{x} > 0.

No normalized residual is assigned to a zero-probability branch. Unnormalized branches suffice for complete-channel calculations.

These formulas are the destructive Born residuals in the supplied Landmark I characterization CheungI (thm:main). The instrument is defined here directly. This does not reproduce that manuscript's uniqueness theorem without its full strategy-class hypotheses.

Displayed formulas in this passage

Hawk04-B@2#eq:Enter · line 676
$E_{S} (ρ) = x \sum ∣ x ⟩ ⟨ x ∣_{K} \otimes M_{x} ρ M_{x}^{†} .$
unlabeled · line 672
$M_{x} = ⟨ x ∣_{S} \otimes I_{T}, x \in {0, 1}^{s} .$
unlabeled · line 686
$p_{x} = ∥ M_{x} ψ ∥^{2}, ψ_{x} = \frac{M _{x} ψ}{p _{x}} if p_{x} > 0.$

Destructive partial readout

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