Manuscript Oai211-A@1 · Oai211-A.tex · section · 3f3e4f63

Three Bell correlations and a complete finite experiment

Three Bell correlations and a complete finite experiment · lines 978–997

For this section $d = 2$ . Let $X, Y, Z$ be the Pauli matrices. The Bell projector is

P_{2} = \frac{I + X \otimes X - Y \otimes Y + Z \otimes Z}{4} .

For a channel $Λ$ , set

c_{x} (Λ) = Tr ((X \otimes X) J_{Λ}), c_{y} (Λ) = Tr ((Y \otimes Y) J_{Λ}), c_{z} (Λ) = Tr ((Z \otimes Z) J_{Λ}) .

Each correlator lies in $[- 1, 1]$ , and

F (Λ) = Tr (P_{2} J_{Λ}) = \frac{1 + c _{x} ( Λ ) - c _{y} ( Λ ) + c _{z} ( Λ )}{4} .

In particular, let $F_{sp} = F (Λ)$ .

Displayed formulas in this passage

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$P_{2} = \frac{I + X \otimes X - Y \otimes Y + Z \otimes Z}{4} .$
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$c_{x} (Λ) = Tr ((X \otimes X) J_{Λ}), c_{y} (Λ) = Tr ((Y \otimes Y) J_{Λ}), c_{z} (Λ) = Tr ((Z \otimes Z) J_{Λ}) .$
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$F (Λ) = Tr (P_{2} J_{Λ}) = \frac{1 + c _{x} ( Λ ) - c _{y} ( Λ ) + c _{z} ( Λ )}{4} .$