Manuscript Hawk03-A@1 · Hawk03-A.tex · section · 9a109c12

Partner, outgoing, and message algebras

One explicit unitary finite benchmark › Partner, outgoing, and message algebras · lines 943–961

Define representations on $R$ by

π_{A} (O) π_{B} (O) π_{M} (O) = J (I_{M} \otimes O_{A} \otimes I_{B}) J^{†}, = J (I_{M} \otimes I_{A} \otimes O_{B}) J^{†} = I_{E} \otimes O_{B}, = J (O_{M} \otimes I_{A} \otimes I_{B}) J^{†} .

Set

A_{in} = π_{A} (B (H_{A})), A_{out} = π_{B} (B (H_{B})), A_{rad} = B (H_{E}) \otimes I_{B} .

Displayed formulas in this passage

unlabeled · line 946
$π_{A} (O) π_{B} (O) π_{M} (O) = J (I_{M} \otimes O_{A} \otimes I_{B}) J^{†}, = J (I_{M} \otimes I_{A} \otimes O_{B}) J^{†} = I_{E} \otimes O_{B}, = J (O_{M} \otimes I_{A} \otimes I_{B}) J^{†} .$
unlabeled · line 956
$A_{in} = π_{A} (B (H_{A})), A_{out} = π_{B} (B (H_{B})), A_{rad} = B (H_{E}) \otimes I_{B} .$