Manuscript X-J-ST@1 · X-J-ST.tex · section · 8f0d1a36

The retained amplitude family

Section B: selective amplitude visibility › The retained amplitude family · lines 1006–1037

X-J-ST@1#eq:amplitude, X-J-ST@1#eq:bloch

For $σ > 0$ , set

p (z) = \frac{1 + tanh ( z / σ )}{2}, ∣ e_{σ} (z)⟩ = 1 - p (z) ∣ 0 ⟩ + p (z) ∣ 1 ⟩, τ_{σ} (z) = ∣ e_{σ} (z)⟩ ⟨ e_{σ} (z)∣ .

The scale $σ$ has the units of $z$ .

Let

D = ∣ 1 ⟩ ⟨ 1 ∣ - ∣ 0 ⟩ ⟨ 0 ∣, X = ∣ 0 ⟩ ⟨ 1 ∣ + ∣ 1 ⟩ ⟨ 0 ∣, t (z) = tanh (z / σ), s (z) = sech (z / σ) .

Then

τ_{σ} (z) = \frac{1}{2} (I + t (z) D + s (z) X) .

This is the amplitude family of X-Enter/X-Enter-ST, used here with the separately constructed coefficient XEnter,XEnterST. Its input is a supplied finite encoding, not an unknown continuum field.

Displayed formulas in this passage

X-J-ST@1#eq:amplitude · line 1009
$p (z) = \frac{1 + tanh ( z / σ )}{2}, ∣ e_{σ} (z)⟩ = 1 - p (z) ∣ 0 ⟩ + p (z) ∣ 1 ⟩, τ_{σ} (z) = ∣ e_{σ} (z)⟩ ⟨ e_{σ} (z)∣ .$
X-J-ST@1#eq:bloch · line 1027
$τ_{σ} (z) = \frac{1}{2} (I + t (z) D + s (z) X) .$
unlabeled · line 1020
$D = ∣ 1 ⟩ ⟨ 1 ∣ - ∣ 0 ⟩ ⟨ 0 ∣, X = ∣ 0 ⟩ ⟨ 1 ∣ + ∣ 1 ⟩ ⟨ 0 ∣, t (z) = tanh (z / σ), s (z) = sech (z / σ) .$

The retained amplitude family

Displayed formulas in this passage

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