Manuscript En01-A@1 · En01-A.tex · definition · 558b972b

Definition: Interface channel

Exact channel, subsystem, and algebraic interfaces · lines 1052–1061

En01-A@1#def:channel

An interface channel is a CPTP map $Λ : B (H_{Q}) \to B (K)$ . An input effect is available after $Λ$ if it equals $Λ^{*} (M)$ for an output effect $M$ . Define

δ_{J} (Λ) = \frac{1}{2} ∥Λ (X_{J}) ∥_{1} .

Displayed formulas in this passage

unlabeled · line 1058
$δ_{J} (Λ) = \frac{1}{2} ∥Λ (X_{J}) ∥_{1} .$

Nearby in this section

lemma: Lemma: Helstrom optimization
section: Exact channel, subsystem, and algebraic interfaces
lemma: Lemma: Hermitian trace-norm contractivity
theorem: Theorem: Channel-interface theorem
corollary: Corollary: Data processing
corollary: Corollary: Exact subsystem interface theorem
lemma: Lemma: Finite-dimensional conditional expectation
corollary: Corollary: Exact algebraic interface theorem