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

Combining the task clock and an amplitude program

Stage D: complete instruments for supplied evaluations › Combining the task clock and an amplitude program · lines 962–994

X-Enter-ST@1#eq:combined

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If a task selects a finite amplitude program, regard $A$ initially as containing its signal input $Q_{a}$ and a passive residual $A_{0}$ . For common padded output interfaces, the combined map is

N (X) = j, y \sum ∣ j, q_{j}, y ⟩ ⟨ j, q_{j}, y ∣_{R} \otimes (Φ_{y}^{(j)} \otimes id_{A_{0}}) (D_{j} X D_{j}^{†}) .

It is CPTP by composition and Lemma lem:paths. Its complete Kraus maps and reference extensions are therefore explicit.

This formula does not give free access to a gauge-dependent task selector. During an orbit comparison the apparatus, task choice, gates, and external preparations are frozen. If a label or residual varies with $a$ , it must be included in the encoding and complete output. The orbit theorem then applies to the resulting complete scalar-input map.

Returning an unmeasured $τ (a)$ while reporting a constant bit is not erasure. It gives the varying output

∣ 0 ⟩ ⟨ 0 ∣_{R} \otimes τ (a) .

A carried qubit is also not Option B's independent classical reference coefficient XEnter.

Displayed formulas in this passage

X-Enter-ST@1#eq:combined · line 968
$N (X) = j, y \sum ∣ j, q_{j}, y ⟩ ⟨ j, q_{j}, y ∣_{R} \otimes (Φ_{y}^{(j)} \otimes id_{A_{0}}) (D_{j} X D_{j}^{†}) .$
unlabeled · line 989
$∣ 0 ⟩ ⟨ 0 ∣_{R} \otimes τ (a) .$