Manuscript Hawk05-C@1 · Hawk05-C.tex · section · ba0719f1

Destructive Enter

Complete interfaces and the two return types › Destructive Enter · lines 434–451

For a basis ${∣ y ⟩}$ of a measured factor $A$ , define

(Enter_{A} \otimes id_{K}) (X) = y \sum ∣ y ⟩ ⟨ y ∣_{Y} \otimes (⟨ y ∣_{A} \otimes I_{K}) X (∣ y ⟩_{A} \otimes I_{K}) .

The measured name $A$ is not returned. Its complete dilation can be

∣ y ⟩_{A} ⟼ ∣ y ⟩_{Y} ∣ y ⟩_{L},

with $L$ unreturned. A continuation with joint access to $Y L$ would have a different quantum interface.

Displayed formulas in this passage

unlabeled · line 437
$(Enter_{A} \otimes id_{K}) (X) = y \sum ∣ y ⟩ ⟨ y ∣_{Y} \otimes (⟨ y ∣_{A} \otimes I_{K}) X (∣ y ⟩_{A} \otimes I_{K}) .$
unlabeled · line 445
$∣ y ⟩_{A} ⟼ ∣ y ⟩_{Y} ∣ y ⟩_{L},$