Manuscript En03-A@1 · En03-A.tex · theorem · 5398614e

Theorem: Exact record compatibility

Scale, records, and residual instruments › Effect pullback · lines 2331–2346 · proof included or linked

En03-A@1#thm:pullback, En03-A@1#eq:pullback

The laws in eq:record-laws agree for every input state and outcome if and only if

T^{*} (E_{w}) = Π_{w} (w \in W) .

Proof. Their difference is $Tr (ρ [T^{*} (E_{w}) - Π_{w}])$ . The bracket is Hermitian. Testing its eigenvector states proves that zero expectation for every state is equivalent to its vanishing.

Displayed formulas in this passage

En03-A@1#eq:pullback · line 2335
$T^{*} (E_{w}) = Π_{w} (w \in W) .$

Nearby in this section

section: Effect pullback
corollary: Corollary: Marginalization