Manuscript VII-G@1 · VII-G.tex · section · 54f561e8

Immediate and coherent implementations that agree

Implementation equivalence and represented readout › Immediate and coherent implementations that agree · lines 1013–1030

VII-G@1#eq:controlled-feedback

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Suppose a source instrument has Kraus operators $M_{a}$ , with $\sum_{a} M_{a}^{†} M_{a} = I$ , and its outcome selects a successor $Γ_{a} (g)$ and unitary $U_{Γ_{a} (g)}$ .

The immediate implementation reads out the pointer of

V_{g}^{src} ψ = a \sum ∣ a ⟩_{A} \otimes M_{a} ψ

and then applies $U_{Γ_{a} (g)}$ . The coherent implementation first applies

C_{g} = a \sum ∣ a ⟩ ⟨ a ∣_{A} \otimes U_{Γ_{a} (g)}

and then reads out $A$ .

Displayed formulas in this passage

VII-G@1#eq:controlled-feedback · line 1025
$C_{g} = a \sum ∣ a ⟩ ⟨ a ∣_{A} \otimes U_{Γ_{a} (g)}$
unlabeled · line 1020
$V_{g}^{src} ψ = a \sum ∣ a ⟩_{A} \otimes M_{a} ψ$

Nearby in this section

proposition: Proposition: Exact source–feedback readout equivalence
section: Immediate and coherent implementations that agree