Manuscript XXII-D@1 · XXII-D.tex · section · 17889d18

Complete-channel transport and error assembly

Complete-channel transport and error assembly · lines 743–757

All channels in this section are completely positive and trace preserving on their stated finite-dimensional interfaces. Use

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

The diamond norm compares channels completely, including an untouched reference Watrous (Chapter 3). It is not assigned to an arbitrary process-matrix probability functional.

Displayed formulas in this passage

unlabeled · line 748
$d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥Φ - Ψ ∥_{⋄}, d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1} .$