Manuscript Hawk07-B@1 · Hawk07-B.tex · proposition · b9785538

Proposition: Entanglement alone cannot signal

Hybrid communication and causal limitations · lines 1521–1533 · proof included or linked

Hawk07-B@1#prop:nosignal

For every bipartite state and every CPTP local operation,

Tr_{A} [(Λ_{A} \otimes id_{B}) (ρ_{A B})] = Tr_{A} ρ_{A B} .

Proof. For a $B$ -observable $Z$ , the adjoint pullback is $Λ_{A}^{*} (I_{A}) \otimes Z = I_{A} \otimes Z$ . Thus all receiver expectations agree.

Displayed formulas in this passage

unlabeled · line 1524
$Tr_{A} [(Λ_{A} \otimes id_{B}) (ρ_{A B})] = Tr_{A} ρ_{A B} .$