Loss of coherence in an optical cat state
= Loss of coherence in an optical cat state
{title2=$s_{\rm env}=e^{-2(1-\eta)|\alpha|^2}$}
A pure-loss channel of transmissivity $\eta$ maps the two branches to system amplitudes $\pm\sqrt\eta\alpha$ and environment amplitudes $\pm\sqrt{1-\eta}\alpha$. Tracing over the environment multiplies their cross terms by its branch overlap, the factor displayed. Large cat states can therefore lose interference rapidly even while their mean <intensities> change only moderately.