Can someone help me prove that [itex]tr(\rho^2) \leq 1[/itex] ?(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Proof of trace of density matrix in pure/mixed states

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