- #1

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Using that [tex]\rho = \sum_i p_i | \psi_i \rangle \langle \psi_i |[/tex]

[tex]\rho^2 = \sum_i p_i^2 | \psi_i \rangle \langle \psi_i |[/tex]

[tex]tr(\rho^2) = \sum_{i, j} p_i^2 \langle j | \psi_i \rangle \langle \psi_i | j \rangle[/tex]

Where do I go from here? Thanks guys.