  Entanglement is a powerful resource for processing quantum information. In
this context pure, maximally entangled states have received considerable
attention. In the case of bipartite qubit-systems the four orthonormal
Bell-states are of this type. One of these Bell states, the singlet Bell-state,
has the additional property of being antisymmetric with respect to particle
exchange. In this contribution we discuss possible generalizations of this
antisymmetric Bell-state to cases with more than two particles and with
single-particle Hilbert spaces involving more than two dimensions. We review
basic properties of these totally antisymmetric states. Among possible
applications of this class of states we analyze a new quantum key sharing
protocol and methods for comparing quantum states.
