Manuscript X-Enter-ST@1 · X-Enter-ST.tex · proposition · f76acc1f

Proposition: Report observables and acquisition

Stage D: complete instruments for supplied evaluations › No acquisition and no universal clock return · lines 997–1020 · proof included or linked

X-Enter-ST@1#prop:noacquisition

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The instrument constructs finite report observables, not an apparatus for acquiring $c_{ε}$ or $a$ from unknown continuum fields.

Proof. For displayed real report values $a_{j}$ , the bounded output observable

B_{R} = j \sum a_{j} ∣ j, q_{j} ⟩ ⟨ j, q_{j} ∣_{R}

has pullback

M^{*} (B_{R} \otimes I_{A}) = j \sum a_{j} ∣ τ_{j} ⟩ ⟨ τ_{j} ∣_{C} \otimes I_{A} .

This is an observable of the installed finite task encoding. The input and Kraus maps contain no field-to-register acquisition map. Different hypothetical continuum inputs with the same supplied finite input therefore produce the same output.

Displayed formulas in this passage

unlabeled · line 1007
$B_{R} = j \sum a_{j} ∣ j, q_{j} ⟩ ⟨ j, q_{j} ∣_{R}$
unlabeled · line 1011
$M^{*} (B_{R} \otimes I_{A}) = j \sum a_{j} ∣ τ_{j} ⟩ ⟨ τ_{j} ∣_{C} \otimes I_{A} .$

Proposition: Report observables and acquisition

Displayed formulas in this passage

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