Manuscript En07-B@1 · En07-B.tex · definition · 45dff4a1

Definition: Destructive computational-basis Enter

Enter, forgetting, and surviving quantum registers · lines 593–611

En07-B@1#def:enter

Let $B$ have computational basis ${∣ j ⟩}_{j = 0}^{m - 1}$ , and let $K$ be a classical record register with the same labels. For any unmeasured register $A$ , define

(id_{A} \otimes Enter_{B}) (X) = j \sum X_{j j} \otimes ∣ j ⟩ ⟨ j ∣_{K},

where

X_{j k} = (I_{A} \otimes ⟨ j ∣) X (I_{A} \otimes ∣ k ⟩) .

The output has no surviving quantum register named $B$ . The map $Drop_{K}$ is partial trace over the record.

Displayed formulas in this passage

unlabeled · line 598
$(id_{A} \otimes Enter_{B}) (X) = j \sum X_{j j} \otimes ∣ j ⟩ ⟨ j ∣_{K},$
unlabeled · line 604
$X_{j k} = (I_{A} \otimes ⟨ j ∣) X (I_{A} \otimes ∣ k ⟩) .$

Nearby in this section

section: Enter, forgetting, and surviving quantum registers
lemma: Lemma: Readout-and-drop equals partial trace
remark: Remark: The dilation is not the classical interface
proposition: Proposition: Operational discard does not entail annihilation