Manuscript Hawk07-A@1 · Hawk07-A.tex · section · f9c0f5da

Enter records cannot turn over

Coherent entropy, classical records, and the dimension neck › Enter records cannot turn over · lines 1234–1250

For a measured factor $A$ in a declared basis, define

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

With surviving quantum factors $E$ , use

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

The name $A$ is consumed. The surviving $E$ is not.

Displayed formulas in this passage

unlabeled · line 1237
$Enter_{A} (X) = y \sum ⟨ y ∣ X ∣ y ⟩ ∣ y ⟩ ⟨ y ∣_{Y} .$
unlabeled · line 1243
$(Enter_{A} \otimes id_{E}) (X) = y \sum ∣ y ⟩ ⟨ y ∣_{Y} \otimes (⟨ y ∣_{A} \otimes I_{E}) X (∣ y ⟩_{A} \otimes I_{E}) .$