  We present protocols for multiparty data hiding of quantum information that
implement all possible threshold access structures. Closely related to secret
sharing, data hiding has a more demanding security requirement: that the data
remain secure against unrestricted LOCC attacks. In the limit of hiding a large
amount of data, our protocols achieve an asymptotic rate of one hidden qubit
per local physical qubit. That is, each party holds a share that is the same
size as the hidden state to leading order, with accuracy and security
parameters incurring an overhead that is asymptotically negligible. The data
hiding states have very unusual entanglement properties, which we briefly
discuss.
