Can anyone help me understand the QFI derivation being done in Appendix C of this paper? The density matrix $\rho = \frac12(|\psi_1\rangle\langle\psi_1|+|\psi_2\rangle\langle\psi_2|)$. I understand that $|\psi_1\rangle$ and $\psi_2\rangle$ are non-orthogonal states so they find eigenvectors that are orthogonal and span the derivatives of $\rho$ to properly calculate the SLD (Symmetric Logarithmic derivative). But density matrix is a $2\times2$ matrix so how am I getting four eigenstates? I am not sure how they are deriving QFI and especially $|e_1\rangle,|e_2\rangle,|e_3\rangle$, and $|e_4\rangle$.
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3$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotCommented Jul 28 at 6:12
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