  We calculate the entanglement of formation and the entanglement of
distillation for arbitrary mixtures of the zero spin states on an
arbitrary-dimensional bipartite Hilbert space. Such states are relevant to
quantum black holes and to decoherence-free subspaces based communication. The
two measures of entanglement are equal and scale logarithmically with the
system size. We discuss its relation to the black hole entropy law. Moreover,
these states are locally distinguishable but not locally orthogonal, thus
violating a conjecture that the entanglement measures coincide only on locally
orthogonal states. We propose a slightly weaker form of this conjecture.
Finally, we generalize our entanglement analysis to any unitary group.
