Manuscript VII-J@1 · VII-J.tex · definition · d8c01b04

Definition: Reference-assisted signalling

Finite channels and operational influence › Admissible interventions · lines 347–367

VII-J@1#def:signal, VII-J@1#eq:signal

Let $R$ be an arbitrary finite untouched reference. Define

Sig_{Φ} (A \to B) = \frac{1}{2} R, ρ, I_{A}, J_{A} sup (Φ_{B} \otimes id_{R}) [(I_{A} \otimes id_{A^{c} R}) (ρ) - (J_{A} \otimes id_{A^{c} R}) (ρ)]_{1} .

The observer receives $B$ and the untouched reference $R$ . Thus $0 \leq Sig_{Φ} \leq 1$ .

Displayed formulas in this passage

VII-J@1#eq:signal · line 350
$Sig_{Φ} (A \to B) = \frac{1}{2} R, ρ, I_{A}, J_{A} sup (Φ_{B} \otimes id_{R}) [(I_{A} \otimes id_{A^{c} R}) (ρ) - (J_{A} \otimes id_{A^{c} R}) (ρ)]_{1} .$