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In this paper, we consider the local unitary classification of the class ofqudit bipartite mixed states for which no information can be obtained locally.These states are represented by symmetrical density matrices in which bothtracial states are maximally mixed. Interestingly, this symmetry facilitatesthe local unitary classification of two-qubit states. However, the sameformalism fails in the case of systems of higher dimensions. We consider abroader set of states by introducing a family of qudit bipartite mixed stateswith maximally mixed marginals. For this family of states, we determine severalconstants which are in variant under local unitary transformations so can beused for entanglement classification. Finally, we consider the two-qutrit caseand in particular, a two-parameter family of states for which the local unitaryclassification is complete. We relate this classification to known entanglementmeasures such as purity and negativity.

Toy model for the correlation of qudit bipartite states with maximally mixed marginals