Manuscript Oai265-A@2 · Oai265-A.tex · section · c0a34a45

A separate, explicitly defined qubit procedure

Finite memory certification is not entropy calibration › A separate, explicitly defined qubit procedure · lines 1619–1644

Let $Λ : C^{2} \to C^{2}$ be one implemented deterministic decoder channel, including all its branches. Define

ω = (id \otimes Λ) (∣ Ω_{2} ⟩ ⟨ Ω_{2} ∣), f = ⟨ Ω_{2} ∣ ω ∣ Ω_{2} ⟩ .

The Bell projector obeys

∣ Ω_{2} ⟩ ⟨ Ω_{2} ∣ = \frac{1}{4} (I \otimes I + X \otimes X - Y \otimes Y + Z \otimes Z) .

Measure the three oriented observables

P_{1} = X \otimes X, P_{2} = - Y \otimes Y, P_{3} = Z \otimes Z

on separate independent preparations. If their ideal means are $r_{s}$ , then

f = \frac{1 + r _{1} + r _{2} + r _{3}}{4} .

Displayed formulas in this passage

unlabeled · line 1623
$ω = (id \otimes Λ) (∣ Ω_{2} ⟩ ⟨ Ω_{2} ∣), f = ⟨ Ω_{2} ∣ ω ∣ Ω_{2} ⟩ .$
unlabeled · line 1629
$∣ Ω_{2} ⟩ ⟨ Ω_{2} ∣ = \frac{1}{4} (I \otimes I + X \otimes X - Y \otimes Y + Z \otimes Z) .$
unlabeled · line 1634
$P_{1} = X \otimes X, P_{2} = - Y \otimes Y, P_{3} = Z \otimes Z$
unlabeled · line 1641
$f = \frac{1 + r _{1} + r _{2} + r _{3}}{4} .$