Manuscript XXII-F@1 · XXII-F.tex · section · 67821705

Complete-channel approximation corollary

Complete-channel approximation corollary · lines 1088–1101

All maps in this section are CPTP on their stated finite-dimensional interfaces. Set

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

The diamond norm includes untouched references and contracts under channel pre- and postcomposition Watrous (Chapter 3). No diamond norm is assigned to an unspecified process-matrix probability functional.

Displayed formulas in this passage

unlabeled · line 1092
$d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥Φ - Ψ ∥_{⋄}, d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1} .$

Nearby in this section

lemma: Lemma: Compatible complete-channel telescoping
section: Complete-channel approximation corollary
corollary: Corollary: Conditional operational approximation
section: Complete-channel approximation corollary