Manuscript XIX-C@1 · XIX-C.tex · section · 98b067d9

A destructive record is not its residual state

Records, residual source functionals, and token acquisition › A destructive record is not its residual state · lines 438–460

XIX-C@1#eq:readout

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For finite factors $S, B$ , the declared computational-basis destructive readout is

M_{S} (ρ) = z \sum ∣ z ⟩ ⟨ z ∣_{R} \otimes (⟨ z ∣_{S} \otimes I_{B}) ρ (∣ z ⟩_{S} \otimes I_{B}) .

The output factors are $R, B$ ; the measured factor $S$ is consumed. The record probabilities and unnormalized residuals are

p_{z} = Tr ((⟨ z ∣_{S} \otimes I_{B}) ρ (∣ z ⟩_{S} \otimes I_{B})), ρ_{B, z}^{un} = (⟨ z ∣_{S} \otimes I_{B}) ρ (∣ z ⟩_{S} \otimes I_{B}) .

These finite record conventions agree with the operational interfaces discussed by Cheung CheungI,CheungEnter,CheungXVIIIA. No uniqueness characterization of measurement is used here.

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XIX-C@1#eq:readout · line 442
$M_{S} (ρ) = z \sum ∣ z ⟩ ⟨ z ∣_{R} \otimes (⟨ z ∣_{S} \otimes I_{B}) ρ (∣ z ⟩_{S} \otimes I_{B}) .$
unlabeled · line 450
$p_{z} = Tr ((⟨ z ∣_{S} \otimes I_{B}) ρ (∣ z ⟩_{S} \otimes I_{B})), ρ_{B, z}^{un} = (⟨ z ∣_{S} \otimes I_{B}) ρ (∣ z ⟩_{S} \otimes I_{B}) .$

A destructive record is not its residual state

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