Statistics of orbital entanglement for the full scattering state in a chaotic quantum dot

We study the statistical properties of orbital entanglement for the full scattering state in a chaotic quantum dot attached to two nonideal two-channel leads via random matrix theory. Using the entanglement entropy as the entanglement quantifier, we obtain its average and probability density function varying the opacity of each lead in the presence and absence of time-reversal symmetry by two methods: (a) exact integration over random matrix ensembles when one contact is ideal and (b) random matrix simulations for arbitrary opacity values. All results show that these two methods are in agreement with each other. The Person correlation coefficient between the entanglement entropy and the entanglement production factor was also analyzed. We verify that the latter predicts a good level of entanglement of the full scattering state.