Manuscript X-H-ST@1 · X-H-ST.tex · section · 943aa27e

The encoded report is not a field observable

Complete destructive instruments for the two dictionaries › The encoded report is not a field observable · lines 1546–1563

X-H-ST@1#eq:reportobservable

For a chosen rational displayed value $a_{j}$ of each report, the bounded register observable is

B_{rep} = j \sum a_{j} ∣ j, q_{j} ⟩ ⟨ j, q_{j} ∣_{R} .

The Heisenberg pullback is

M_{cl}^{*} (B_{rep} \otimes I_{A}) = j \sum a_{j} ∣ τ_{j} ⟩ ⟨ τ_{j} ∣_{C} \otimes I_{A} .

It is an observable of the finite task encoding.

Displayed formulas in this passage

X-H-ST@1#eq:reportobservable · line 1555
$M_{cl}^{*} (B_{rep} \otimes I_{A}) = j \sum a_{j} ∣ τ_{j} ⟩ ⟨ τ_{j} ∣_{C} \otimes I_{A} .$
unlabeled · line 1550
$B_{rep} = j \sum a_{j} ∣ j, q_{j} ⟩ ⟨ j, q_{j} ∣_{R} .$