Supersinglets

Supersinglets $|{\cal S}_N^{(d)}>$ are states of total spin zero of $N$ particles of $d$ levels. Some applications of the $|{\cal S}_N^{(N)}>$ and $|{\cal S}_N^{(2)}>$ states are described. The $|{\cal S}_N^{(N)}>$ states can be used to solve three problems which have no classical solution: The "$N$ strangers," "secret sharing," and "liar detection" problems. The $|{\cal S}_N^{(2)}>$ (with $N$ even) states can be used to encode qubits in decoherence-free subspaces.