= Dephased Bell-state mixture
{title2=$\rho_\alpha=\frac{1+\alpha}{2}|\Phi^+\rangle\langle\Phi^+|+\frac{1-\alpha}{2}|\Phi^-\rangle\langle\Phi^-|$}
For real $-1\leq\alpha\leq1$, this two-<qubit> <density operator> has equal $00$ and $11$ populations and off-diagonal coherences $\alpha/2$. It is a <pure state> exactly when $\alpha=\pm1$, and a <separable quantum state> exactly when $\alpha=0$. Its <partial transpose> has <eigenvalues> $1/2,1/2,\alpha/2,-\alpha/2$, directly witnessing entanglement for every nonzero admissible coherence.
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