Manuscript En07-C@1 · En07-C.tex · definition · 3f7e9ebb

Definition: Destructive basis Enter

Destructive Enter, forgetting, and classical records · lines 662–681

En07-C@1#def:enter, En07-C@1#eq:enter

Choose an orthonormal basis ${∣ z ⟩}$ of $B$ , set

M_{z} = I_{R} \otimes ⟨ z ∣_{B} : R \otimes B \to R,

and define

Enter_{B} (X) = z \sum M_{z} X M_{z}^{†} \otimes ∣ z ⟩ ⟨ z ∣_{Z}, Enter_{B} : L (R \otimes B) \to L (R \otimes Z) .

The record $Z$ is classical: the output is diagonal in its declared basis. The measured quantum factor $B$ is not returned. Forgetting the record is $Drop_{Z} = Tr_{Z}$ .

Displayed formulas in this passage

En07-C@1#eq:enter · line 669
$Enter_{B} (X) = z \sum M_{z} X M_{z}^{†} \otimes ∣ z ⟩ ⟨ z ∣_{Z}, Enter_{B} : L (R \otimes B) \to L (R \otimes Z) .$
unlabeled · line 665
$M_{z} = I_{R} \otimes ⟨ z ∣_{B} : R \otimes B \to R,$

Nearby in this section

section: Destructive Enter, forgetting, and classical records
section: Destructive Enter, forgetting, and classical records
lemma: Lemma: Enter followed by Drop equals partial trace
proposition: Proposition: Operational discard is not annihilation
section: Destructive Enter, forgetting, and classical records
theorem: Theorem: Record-only recovery obstruction
section: Destructive Enter, forgetting, and classical records