Manuscript En05-B@1 · En05-B.tex · section · 8b626460

Finite hybrid interfaces

Complete instruments, locality, and comparison › Finite hybrid interfaces · lines 266–286

This is the controller-support convention of VII-G and En05-A CheungVIIG,CheungEn05A. A schedule or routing plan chosen from an unknown state description is not admitted.

For finite region $I$ , write $R_{I}$ for restriction to its complete interface, tracing quantum factors and summing classical blocks outside $I$ . The reduced state $R_{I} ω$ is its snapshot.

We use

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

For finite hybrid interfaces the diamond norm is the corresponding completely bounded trace norm, allowing arbitrary reference extensions.

Displayed formulas in this passage

unlabeled · line 278
$d_{⋄} (Φ, Ψ) = \frac{1}{2} ∥ Φ - Ψ ∥_{⋄}, d_{tr} (ρ, σ) = \frac{1}{2} ∥ ρ - σ ∥_{1} .$

Nearby in this section

section: Finite hybrid interfaces
assumption: Assumption: Declared local control
lemma: Lemma: Snapshot, channel, and adjoint comparison