  We study numerically the production of orbital and spin entangled states in
chaotic quantum dots for non-interacting electrons. The introduction of
spin-orbit coupling permit us to identify signatures of time-reversal symmetry
correlations in the entanglement production previously unnoticed, resembling
weak-(anti)localization quantum corrections to the conductance. We find the
entanglement to be strongly dependent on spin-orbit coupling, showing universal
features for broken time-reversal and spin-rotation symmetries.
