Manuscript En10-B@1 · En10-B.tex · section · a1105bad

A complete statistical contract

Calibration and complete-record finite-shot inference › A complete statistical contract · lines 737–747

For states and channels use

d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Λ, Γ) = \frac{1}{2} ∥ Λ - Γ ∥_{⋄} .

For classical laws, $d_{TV} (P, Q) = \frac{1}{2} \sum_{r} ∣ P (r) - Q (r) ∣$ . An expectation of a function in $[0, 1]$ changes by at most total variation.

Displayed formulas in this passage

unlabeled · line 740
$d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1}, d_{⋄} (Λ, Γ) = \frac{1}{2} ∥ Λ - Γ ∥_{⋄} .$

Nearby in this section

assumption: Assumption: Conditional fixed-shot acquisition
section: A complete statistical contract