= Concurrence of a two-qubit Werner state
{title2=$C(W_F)=2F-1,\quad 1/2<F\leq1$}
For any normalized pure two-<qubit> vector, its squared overlap with a <maximally entangled state> is at most $(1+C)/2$: in a <Schmidt decomposition> the overlap is bounded by $(\sqrt\lambda+\sqrt{1-\lambda})/\sqrt2$. Averaging gives $C(W_F)\geq2F-1$. Equality follows from the six-state ensemble $\sqrt F\,|\Psi_-\rangle\pm\sqrt{1-F}\,|t_j\rangle$, with equal weights, where $t_1=\Psi_+$, $t_2=\Phi_-$ and $t_3=i\Phi_+$. The coherences cancel and each coefficient determinant gives pure concurrence $2F-1$.
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