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\begin{equation*}
\sigma_{\alpha} = {2\over 7}|\psi_+\rangle\langle\psi_+| + {\alpha\over 7}\sigma_+ +
{{5 - \alpha}\over 7} \sigma_- \quad for \quad 2\leq \alpha \leq 5,
\end{equation*}
\end{document}