  We study the conditions when mixtures of entangled pure states with maximally
mixed one-qudit reduced density matrices remain entangled. We found that the
resulting mixed state remains entangled when the number of entangled pure
states to be mixed is less than or equal to the dimension of the pure states.
For the latter case of mixing a number of pure states equal to their dimension,
we found that the mixed state is entangled provided that the entangled pure
states to be mixed are not equally weighted. We also found that one can
restrict the set of pure states that one can mix from in order to ensure that
the resulting mixed state is genuinely entangled.
