The next term appears in my research and it is quite meaningful: $\sqrt{\rho_{ee}\rho_{gg}}$-|$\rho_{eg}$| Where $\rho_{gg}$ and $\rho_{ee}$ are the populations in the excited and ground states, and $\rho_{eg}$ is the transition probability between ground and excited. The problem is that I have no idea what physical meaning it has. Is exactly one of the eigenvalues of the matrix $R=\sqrt{\sqrt{\rho}\tilde{\rho}\sqrt{\rho}}$ with $\tilde{\rho}=(\sigma_y \otimes \sigma_y)\rho^*(\sigma_y \otimes \sigma_y)$, but I dont know what does its eigenvalues mean either.

I promise a mention in the paper to whoever helps me with this :D

  • $\begingroup$ As a note the trace of your R is the fidelity of the quantum states rho and rho tilde. This is basically a measure of how close these states are. Sometimes the fidelity is also defined as the square of the trace of R. Maybe this will turn out to be helpful. $\endgroup$ – Zarathustra Jun 10 at 22:13

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