Manuscript VIII-ST@1 · VIII-ST.tex · section · fe979f3b

Fixed-table complete-channel approximation

One destructive clock and complete table instruments › Fixed-table complete-channel approximation · lines 1938–1955

VIII-ST@1#eq:table-instrument

For a finite code set $X$ , let $L_{a, y}$ be known diagonal matrices,

L_{a, y} = x \in X \sum ℓ_{a, y} (x) ∣ x ⟩ ⟨ x ∣, y \sum ∣ ℓ_{a, y} (x) ∣^{2} = 1.

They encode already-defined certificate scores or readout choices, not an unknown continuum observable. The complete clock–table instrument is

I (X) = a, y \sum ∣ a ⟩ ⟨ a ∣_{R} \otimes ∣ y ⟩ ⟨ y ∣_{Y} \otimes L_{a, y} D_{a} X D_{a}^{†} L_{a, y}^{†} .

Displayed formulas in this passage

VIII-ST@1#eq:table-instrument · line 1949
$I (X) = a, y \sum ∣ a ⟩ ⟨ a ∣_{R} \otimes ∣ y ⟩ ⟨ y ∣_{Y} \otimes L_{a, y} D_{a} X D_{a}^{†} L_{a, y}^{†} .$
unlabeled · line 1942
$L_{a, y} = x \in X \sum ℓ_{a, y} (x) ∣ x ⟩ ⟨ x ∣, y \sum ∣ ℓ_{a, y} (x) ∣^{2} = 1.$