Manuscript X-L-ST@1 · X-L-ST.tex · section · 20a32a22

A concrete amplitude report

Recovery of complete residual-report instruments › A concrete amplitude report · lines 1618–1636

For an ordinary supplied real number $a$ , fix an encoding scale $σ_{e} > 0$ , distinct from $ε$ , and define

p (a) = \frac{1 + tanh ( a / σ _{e} )}{2},

∣ e (a)⟩ = 1 - p (a) ∣ 0 ⟩ + p (a) ∣ 1 ⟩, τ (a) = ∣ e (a)⟩ ⟨ e (a)∣ .

This is the finite amplitude shape used in X-Enter-ST XEnterST. It is a preparation from supplied data, not a continuum acquisition map.

Displayed formulas in this passage

unlabeled · line 1623
$p (a) = \frac{1 + tanh ( a / σ _{e} )}{2},$
unlabeled · line 1626
$∣ e (a)⟩ = 1 - p (a) ∣ 0 ⟩ + p (a) ∣ 1 ⟩, τ (a) = ∣ e (a)⟩ ⟨ e (a)∣ .$