Manuscript Em03-G@1 · Em03-G-v1.tex · section · 0bb3a8a3

The complete scalar radiation channel

The complete scalar radiation channel · lines 644–669

Em03-G@1#eq:matrixfunctional

First define the field-output channel as a map into state functionals:

N_{G} (ρ) (A) = (tr_{S} \otimes ω_{U}) [U_{G}^{†} (I \otimes A) U_{G} (ρ \otimes I)] .

Equivalently, its values on source matrix units $E_{z w} = ∣ z ⟩ ⟨ w ∣$ are

N_{G} (E_{z w}) (A) = x \sum m_{x z} m_{x w} ω_{U} (B_{x w}^{†} A B_{x z}) .

This formulation does not assume a global field density.

For a weighted field coefficient $l$ , write

A_{l} = s (a_{1}, l), B_{l} = s (a_{2}, l) .

Displayed formulas in this passage

Em03-G@1#eq:matrixfunctional · line 655
$N_{G} (E_{z w}) (A) = x \sum m_{x z} m_{x w} ω_{U} (B_{x w}^{†} A B_{x z}) .$
unlabeled · line 648
$N_{G} (ρ) (A) = (tr_{S} \otimes ω_{U}) [U_{G}^{†} (I \otimes A) U_{G} (ρ \otimes I)] .$
unlabeled · line 666
$A_{l} = s (a_{1}, l), B_{l} = s (a_{2}, l) .$