= Schmidt-basis Pauli correlation tensor
{c}
{title2=$T=\operatorname{diag}(s,-s,1)$}
For the <pure state> $\lambda_0|00\rangle+\lambda_1|11\rangle$ with real normalized <Schmidt coefficients>, the two-body <Pauli correlators> form $T=\operatorname{diag}(s,-s,1)$, $s=2\lambda_0\lambda_1$. Thus arbitrary local axes give $\langle(\mathbf a\cdot\sigma)\otimes(\mathbf b\cdot\sigma)\rangle=s(a_xb_x-a_yb_y)+a_zb_z$. The negative $yy$ component follows from the phases in the <Pauli operators>.
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