Quantum states for perfectly secure secret sharing
Dong Pyo Chi, Jeong Woon Choi, Jeong San Kim, Tae‐Wan Kim, Soojoon Lee · Physical Review A · 2008
In this paper, 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.