Entanglement of zero-angular-momentum mixtures and black-hole entropy

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.