  We investigate statistical aspects of the entanglement production for open
chaotic mesoscopic billiards in contact with superconducting parts, known as
Andreev billiards. The complete distributions of concurrence and entanglement
of formation are obtained by using the Altland-Zirnbauer symmetry classes of
circular ensembles of scattering matrices, which complements previous studies
in chaotic universal billiards belonging to other classes of random matrix
theory. Our results show a unique and very peculiar behavior: the realization
of entanglement in a Andreev billiard always results in non-separable state,
regardless of the time reversal symmetry. The analytical calculations are
supported by a numerical Monte Carlo simulation.
