Manuscript En03-A@1 · En03-A.tex · section · 5398614e

Residual instruments

Scale, records, and residual instruments › Residual instruments · lines 2455–2474

En03-A@1#eq:fine-instrument, En03-A@1#eq:coarse-instrument

For the fine PVM, define

F (ρ) = w \sum ∣ w ⟩ ⟨ w ∣_{R} \otimes T z : q (z) = w \sum P_{z} ρ P_{z} .

For a complete coarse instrument, each $I_{w}$ is CP and $\sum_{w} I_{w}$ is trace preserving. Set

G (ρ) = w \sum ∣ w ⟩ ⟨ w ∣_{R} \otimes I_{w} (T (ρ)), E_{w} = I_{w}^{*} (I) .

Both outputs are on $R \otimes H_{L}$ .

Displayed formulas in this passage

En03-A@1#eq:fine-instrument · line 2458
$F (ρ) = w \sum ∣ w ⟩ ⟨ w ∣_{R} \otimes T z : q (z) = w \sum P_{z} ρ P_{z} .$
En03-A@1#eq:coarse-instrument · line 2466
$G (ρ) = w \sum ∣ w ⟩ ⟨ w ∣_{R} \otimes I_{w} (T (ρ)), E_{w} = I_{w}^{*} (I) .$