# Have you ever seen: $\sqrt{\rho_{ee}\rho_{gg}}$-|$\rho_{eg}$|?

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

• 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. – Zarathustra Jun 10 at 22:13