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

Record equality versus residual equality

Named access, residual instruments, and recovery boundaries › Record equality versus residual equality · lines 1132–1147

Let $P_{z}$ be input projectors, let $q$ aggregate their fine outcomes, and put

Δ_{w} (X) = z : q (z) = w \sum P_{z} X P_{z}, R_{w} = z : q (z) = w \sum P_{z} .

For a channel $T$ and an output instrument ${I_{w}}$ , compare

F (X) = w \sum ∣ w ⟩ ⟨ w ∣ \otimes T (Δ_{w} (X)), G (X) = w \sum ∣ w ⟩ ⟨ w ∣ \otimes I_{w} (T (X)) .

Displayed formulas in this passage

unlabeled · line 1136
$Δ_{w} (X) = z : q (z) = w \sum P_{z} X P_{z}, R_{w} = z : q (z) = w \sum P_{z} .$
unlabeled · line 1142
$F (X) = w \sum ∣ w ⟩ ⟨ w ∣ \otimes T (Δ_{w} (X)), G (X) = w \sum ∣ w ⟩ ⟨ w ∣ \otimes I_{w} (T (X)) .$