Manuscript Oai280-C@1 · Oai280-C.tex · section · 7d44b8c0

The three-correlation qubit identity certificate

Finite-confidence certification › The three-correlation qubit identity certificate · lines 1541–1569

For a complete qubit channel define

c_{x} = Tr ((X \otimes X) J (Λ_{0})), c_{y} = Tr ((Y \otimes Y) J (Λ_{0})), c_{z} = Tr ((Z \otimes Z) J (Λ_{0})) .

Since

Φ_{2} = \frac{1}{4} (I + X \otimes X - Y \otimes Y + Z \otimes Z),

its Bell overlap is

f = \frac{1 + c _{x} - c _{y} + c _{z}}{4} .

With independent bounded-outcome estimates and allocations $δ_{i}$ , let

f = \frac{1 + c _{x} - c _{y} + c _{z}}{4}, ζ = \frac{1}{4} i = x, y, z \sum (t_{i} + γ_{i}),

and clip the overlap endpoints to $[0, 1]$ :

f_{L} = max {0, min {1, f - ζ}}, f_{U} = max {0, min {1, f + ζ}} .

Displayed formulas in this passage

unlabeled · line 1544
$c_{x} = Tr ((X \otimes X) J (Λ_{0})), c_{y} = Tr ((Y \otimes Y) J (Λ_{0})), c_{z} = Tr ((Z \otimes Z) J (Λ_{0})) .$
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$Φ_{2} = \frac{1}{4} (I + X \otimes X - Y \otimes Y + Z \otimes Z),$
unlabeled · line 1554
$f = \frac{1 + c _{x} - c _{y} + c _{z}}{4} .$
unlabeled · line 1559
$f = \frac{1 + c _{x} - c _{y} + c _{z}}{4}, ζ = \frac{1}{4} i = x, y, z \sum (t_{i} + γ_{i}),$
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$f_{L} = max {0, min {1, f - ζ}}, f_{U} = max {0, min {1, f + ζ}} .$