Manuscript Hawk04-C@1 · Hawk04-C-v1.tex · definition · 94d46352

Definition: Destructive Enter and classical discard

Row 3: the radiation and readout analogy · lines 752–779

Hawk04-C@1#def:enter, Hawk04-C@1#eq:enter, Hawk04-C@1#eq:drop-bit

Let $S$ be a measured qubit register and $T$ the surviving quantum register. For computational strings $z$ , put

M_{z} = ⟨ z ∣_{S} \otimes I_{T} .

Destructive Enter has the hybrid channel

M_{S} (X) = z \sum ∣ z ⟩ ⟨ z ∣_{K} \otimes M_{z} X M_{z}^{†} .

The output names are $K$ and $T$ , not $S$ . The algebra on $K$ is the diagonal classical algebra.

Classical discard acts on a hybrid block-diagonal operator by

dropBit_{K} (z \sum ∣ z ⟩ ⟨ z ∣_{K} \otimes X_{z}) = z \sum X_{z} .

The notation extends to a finite bit string. It returns no register $K$ .

Displayed formulas in this passage

Hawk04-C@1#eq:enter · line 761
$M_{S} (X) = z \sum ∣ z ⟩ ⟨ z ∣_{K} \otimes M_{z} X M_{z}^{†} .$
Hawk04-C@1#eq:drop-bit · line 771
$dropBit_{K} (z \sum ∣ z ⟩ ⟨ z ∣_{K} \otimes X_{z}) = z \sum X_{z} .$
unlabeled · line 757
$M_{z} = ⟨ z ∣_{S} \otimes I_{T} .$