  The scaling symmetry in conformal quantum mechanics (CQM) can be broken due
to the boundary conditions that follow from the requirement of a unitary time
evolution of the Hamiltonian. We show that the scaling symmetry of CQM can be
restored by introducing a suitable mixed state, which is associated with a
nonvanishing von Neumann entropy. We give an explicit formula for the entropy
arising from the mixed state in CQM. Our work provides a direct link between
the restoration of a broken symmetry and von Neumann entropy.
