  We investigate the asymmetry properties of quantum states in relation to the
Hamiltonian responsible for the magnetic dipolar interaction (MDI) dynamics,
and we evaluate its relationship to entanglement production. We consider some
classes of pure and mixed quantum states of two qubits evolved under MDI and,
using the asymmetry measure defined via the Wigner-Yanase skew information, we
describe the asymmetry dependence on the Hamiltonian parameters and initial
conditions of the system. In addition, we define and calculate the dynamics of
the asymmetry of local states, characterizing their temporal and interaction
parameters dependence. Finally, because the MDI Hamiltonian has a null
eigenvalue, the group generator-based asymmetry measure does not adequately
quantify the state susceptibility with respect to the action of the subspace
generated by the eigenvectors associated with this eigenvalue. For this reason,
we also define and study the group element-based asymmetry measure with
relation to the unitary operator associated with the MDI Hamiltonian.
