Manuscript Hawk07-A@1 · Hawk07-A.tex · section · f9c0f5da

The Haar decoupling calculation

The Haar decoupling calculation · lines 706–728

Use the Bell test

∣ Φ_{d} ⟩_{Q L} = \frac{1}{d} i = 1 \sum^{d} ∣ i ⟩_{Q} ∣ i ⟩_{L} .

At a cut $D = r b$ , set

ω_{QB}^{U} = (id_{Q} \otimes C^{U}) (∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣), σ_{B}^{U} = C^{U} (I_{L} / d),

X_{QB}^{U} = ω_{QB}^{U} - \frac{I _{Q}}{d} \otimes σ_{B}^{U} .

Displayed formulas in this passage

unlabeled · line 710
$∣ Φ_{d} ⟩_{Q L} = \frac{1}{d} i = 1 \sum^{d} ∣ i ⟩_{Q} ∣ i ⟩_{L} .$
unlabeled · line 716
$ω_{QB}^{U} = (id_{Q} \otimes C^{U}) (∣ Φ_{d} ⟩ ⟨ Φ_{d} ∣), σ_{B}^{U} = C^{U} (I_{L} / d),$
unlabeled · line 723
$X_{QB}^{U} = ω_{QB}^{U} - \frac{I _{Q}}{d} \otimes σ_{B}^{U} .$