  In this work, we investigate what kinds of quantum states are feasible to
perform perfectly secure secret sharing, and present its necessary and
sufficient conditions. We also show that the states are bipartite distillable
for all bipartite splits, and hence the states could be distillable into the
Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing
states, which have an arbitrarily small amount of bipartite distillable
entanglement for a certain split.
