Manuscript VII-E-ST@1 · VII-E-ST.tex · section · d28d9c5d

Exact record and instrument criteria

Contract E: readout, records, and residuals › Exact record and instrument criteria · lines 444–458

VII-E-ST@1#eq:event-norm

The following useful error formula is record-only and unassisted:

ρ sup d_{TV} (p_{ρ}^{G}, p_{ρ}^{F}) = A \subseteq W max w \in A \sum (T^{*} (E_{w}) - Π_{w})_{\infty} .

Indeed, total variation is the maximum absolute difference on an outcome event. Interchange the finite maximum with the state supremum and use $sup_{ρ} ∣ Tr (H ρ) ∣ = ∥ H ∥_{\infty}$ for Hermitian $H$ . No equality with an assisted channel error is inferred.

Displayed formulas in this passage

VII-E-ST@1#eq:event-norm · line 447
$ρ sup d_{TV} (p_{ρ}^{G}, p_{ρ}^{F}) = A \subseteq W max w \in A \sum (T^{*} (E_{w}) - Π_{w})_{\infty} .$

Nearby in this section

section: Exact record and instrument criteria
theorem: Theorem: Effect pullback and the full residual criterion
theorem: Theorem: Residual obstruction and its robust form
section: Exact record and instrument criteria