Manuscript VII-E-ST@1 · VII-E-ST.tex · section · d28d9c5d

Contract G: finite completely positive hybrid evolution

Contract G: finite completely positive hybrid evolution · lines 1225–1244

The table $Ψ_{h ∣ g}$ is fixed independently of the current unknown density operator. Matter dependence enters through Born probabilities

p (h ∣ g, ρ) = Tr (E_{h ∣ g} ρ), E_{h ∣ g} = Ψ_{h ∣ g}^{*} (I) .

An undeclared state-dependent compiler is not part of this law.

Composition is explicit:

(Λ \circ Ψ)_{k ∣ g} = h \sum Λ_{k ∣ h} \circ Ψ_{h ∣ g} .

Completeness follows by summing its adjoint effects. Certificates concatenate along the declared paths; this does not create a certificate for a previously uncertified edge.

Displayed formulas in this passage

unlabeled · line 1230
$p (h ∣ g, ρ) = Tr (E_{h ∣ g} ρ), E_{h ∣ g} = Ψ_{h ∣ g}^{*} (I) .$
unlabeled · line 1237
$(Λ \circ Ψ)_{k ∣ g} = h \sum Λ_{k ∣ h} \circ Ψ_{h ∣ g} .$

Nearby in this section

section: Contract G: finite completely positive hybrid evolution
theorem: Theorem: Finite hybrid structure