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

An explicit visible readout

Stage C: the retained finite amplitude trial › An explicit visible readout · lines 719–749

X-Enter-ST@1#eq:TV

Direct destructive readout has

Pr (1 ∣ a) = p (a) .

Its witness discrepancy is

Δ_{ε} := d_{TV} (Law_{read} (c_{ε}), Law_{read} (0)) = \frac{1}{2} tanh (c_{ε} / σ) > 0.

In fact,

\frac{d}{d λ} Pr (1 ∣ λ c_{ε}) = \frac{c _{ε}}{2 σ} sech^{2} (λ c_{ε} / σ) > 0.

Thus this readout detects variation of the encoded gauge coefficient. It does not make that variation gauge invariant XEnter.

For fixed finite $a$ , an ideal mathematical preparation is a one-qubit rotation taking $∣ 0 ⟩$ to $∣ e (a)⟩$ . Installing finitely many such rotations or their approximations is not a construction of a field-to-qubit preparation for arbitrary smooth input data.

Displayed formulas in this passage

X-Enter-ST@1#eq:TV · line 726
$Δ_{ε} := d_{TV} (Law_{read} (c_{ε}), Law_{read} (0)) = \frac{1}{2} tanh (c_{ε} / σ) > 0.$
unlabeled · line 722
$Pr (1 ∣ a) = p (a) .$
unlabeled · line 734
$\frac{d}{d λ} Pr (1 ∣ λ c_{ε}) = \frac{c _{ε}}{2 σ} sech^{2} (λ c_{ε} / σ) > 0.$

An explicit visible readout

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