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

Definition: Accessible comparison

Scale, records, and residual instruments › Accessible output algebras · lines 2603–2614

En03-A@1#def:accessible, En03-A@1#eq:accessible-distance

Outputs agree operationally on $O_{L}$ if all its expectations agree. For channels with the same output interface,

d_{O_{L}} (F, G) = \frac{1}{2} ρ sup A = A^{†} \in O_{L} ∥ A ∥_{\infty} \leq 1 sup ∣ Tr (A [F (ρ) - G (ρ)])∣ .

Displayed formulas in this passage

En03-A@1#eq:accessible-distance · line 2607
$d_{O_{L}} (F, G) = \frac{1}{2} ρ sup A = A^{†} \in O_{L} ∥ A ∥_{\infty} \leq 1 sup ∣ Tr (A [F (ρ) - G (ρ)])∣ .$