Manuscript Oai280-B@1 · Oai280-B.tex · section · 6d92ab75

Choi overlap and reference-preserving conversion

Bell correlations and simultaneous finite-data certification › Choi overlap and reference-preserving conversion · lines 1235–1253

For a qubit channel $Λ$ , set

P_{2} = ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣, J_{Λ} = (id_{Q} \otimes Λ) (P_{2}) .

The Pauli expansion is

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

Define

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

Displayed formulas in this passage

unlabeled · line 1238
$P_{2} = ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣, J_{Λ} = (id_{Q} \otimes Λ) (P_{2}) .$
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$P_{2} = \frac{1}{4} (I + X \otimes X - Y \otimes Y + Z \otimes Z) .$
unlabeled · line 1247
$c_{j} (Λ) = Tr ((σ_{j} \otimes σ_{j}) J_{Λ}), F (Λ) = Tr (P_{2} J_{Λ}) = \frac{1 + c _{x} - c _{y} + c _{z}}{4} .$