Manuscript I@2 · I.tex · section · 85631fa7

One global state

Configurations and specified Born semantics › One global state · lines 469–496

For a finite live-name set $L$ , write

H_{L} = q \in L ⨂ C^{2} .

An ordering is chosen for matrices and bit strings. Changing the ordering simultaneously permutes names and tensor factors.

For $S \subseteq L$ , let $S = L ∖ S$ , and define

P^{S}_{κ} = ∣ κ ⟩ ⟨ κ ∣_{S} \otimes I_{S}, M^{S}_{κ} = ⟨ κ ∣_{S} \otimes I_{S} .

The projector acts on $H_{L}$ , whereas

M^{S}_{κ} : H_{L} ⟶ H_{S}

removes the measured factors. It satisfies

(M^{S}_{κ})^{†} M^{S}_{κ} = P^{S}_{κ} .

Displayed formulas in this passage

unlabeled · line 472
$H_{L} = q \in L ⨂ C^{2} .$
unlabeled · line 480
$P^{S}_{κ} = ∣ κ ⟩ ⟨ κ ∣_{S} \otimes I_{S}, M^{S}_{κ} = ⟨ κ ∣_{S} \otimes I_{S} .$
unlabeled · line 488
$M^{S}_{κ} : H_{L} ⟶ H_{S}$
unlabeled · line 493
$(M^{S}_{κ})^{†} M^{S}_{κ} = P^{S}_{κ} .$