Reduced density operator of a weakly coupled oscillator pair
= Reduced density operator of a weakly coupled oscillator pair
If a weak interaction changes $|0,0\rangle$ to a normalized state proportional to $|0,0\rangle-g|1,1\rangle$, tracing out either oscillator gives eigenvalues $1/(1+g^2)$ and $g^2/(1+g^2)$.