Manuscript Oai280-A@1 · Oai280-A.tex · section · 27038823

Choi overlap and half-diamond conversion

The finite sector-label experiment › Choi overlap and half-diamond conversion · lines 1145–1164

Let

∣ Φ_{2} ⟩ = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2}, P_{2} = ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣, J_{Λ} = (id \otimes Λ) (P_{2}) .

For Pauli matrices $X, Y, Z$ ,

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

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 1148
$∣ Φ_{2} ⟩ = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2}, P_{2} = ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣, J_{Λ} = (id \otimes Λ) (P_{2}) .$
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$P_{2} = \frac{I + X \otimes X - Y \otimes Y + Z \otimes Z}{4} .$
unlabeled · line 1158
$c_{j} (Λ) = Tr ((σ_{j} \otimes σ_{j}) J_{Λ}), F (Λ) = Tr (P_{2} J_{Λ}) = \frac{1 + c _{x} - c _{y} + c _{z}}{4} .$