Manuscript En01-A@1 · En01-A.tex · corollary · 558b972b

Corollary: Questions as hierarchy interfaces

Operator-valued Möbius hierarchy and three orders · lines 1753–1773 · proof included or linked

En01-A@1#cor:question-order

For a measurement channel,

ω_{J} (Λ_{M}) = \frac{1}{2} o \sum ∣ η_{M_{o}} (J) ∣.

For a binary question and nonempty $J$ ,

ω_{J} (Λ_{M}) = ∣ η_{M} (J) ∣, ord (Λ_{M}) = ord (M) .

Proof. Apply the measurement channel to $Z_{J}$ . In the binary case its two diagonal entries are $η_{M} (J)$ and $- η_{M} (J)$ .

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