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

An optional local relational phase package

An optional local relational phase package · lines 1450–1484

X-J-ST@1#eq:phaseinput, X-J-ST@1#eq:phaseinstrument

The independent coefficients also instantiate a restricted two-coefficient comparison. This section does not replace the direct amplitude theorem or strengthen local charge matching to whole-algebra matching.

For $σ_{p} > 0$ , prepare

∣ ψ (b_{1}, b_{2})⟩ = \frac{∣ 0 ⟩ + e ^{i α} ∣ 1 ⟩}{2} \otimes \frac{∣ 0 ⟩ + e ^{i β} ∣ 1 ⟩}{2}, α = \frac{b _{1}}{σ _{p}}, β = \frac{b _{2}}{σ _{p}} .

Define

∣ χ_{\pm} ⟩ = \frac{∣ 01 ⟩ \pm ∣ 10 ⟩}{2} .

For input on the two signals and $A_{fin}$ , put

N_{F} (Z) N_{\pm} (Z) = (⟨ 00 ∣ \otimes I) Z (∣ 00 ⟩ \otimes I) + (⟨ 11 ∣ \otimes I) Z (∣ 11 ⟩ \otimes I), = (⟨ χ_{\pm} ∣ \otimes I) Z (∣ χ_{\pm} ⟩ \otimes I) .

Displayed formulas in this passage

X-J-ST@1#eq:phaseinput · line 1459
$∣ ψ (b_{1}, b_{2})⟩ = \frac{∣ 0 ⟩ + e ^{i α} ∣ 1 ⟩}{2} \otimes \frac{∣ 0 ⟩ + e ^{i β} ∣ 1 ⟩}{2}, α = \frac{b _{1}}{σ _{p}}, β = \frac{b _{2}}{σ _{p}} .$
X-J-ST@1#eq:phaseinstrument · line 1475
$N_{F} (Z) N_{\pm} (Z) = (⟨ 00 ∣ \otimes I) Z (∣ 00 ⟩ \otimes I) + (⟨ 11 ∣ \otimes I) Z (∣ 11 ⟩ \otimes I), = (⟨ χ_{\pm} ∣ \otimes I) Z (∣ χ_{\pm} ⟩ \otimes I) .$
unlabeled · line 1471
$∣ χ_{\pm} ⟩ = \frac{∣ 01 ⟩ \pm ∣ 10 ⟩}{2} .$

An optional local relational phase package

Displayed formulas in this passage

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