  Locally indistinguishable states are useful to distribute information among
spatially separated parties such that the information is locked. This implies
that the parties are not able to extract the information completely via local
operations and classical communication (LOCC) while it might be possible via
LOCC when the parties share entanglement. In this work, we consider an
information distribution protocol using orthogonal states for m >= 3 spatially
separated parties such that even if any k <= (m-1) parties collaborate still
the information cannot be revealed completely. Such a protocol is useful to
understand up to what extent the encoded information remains locked. However,
if required, the parties can share entanglement and extract the information
completely by LOCC. To make the process resource efficient, it should consume
less number of entangled states. We show that though the set of states, which
are locally indistinguishable across every bipartition, are sufficient for the
above protocol, they may consume higher number of entangled states when aiming
for complete information extraction. We establish this by constructing a class
of locally indistinguishable sets of orthogonal states which can be employed to
accomplish the above protocol and these sets consume less number of entangled
states, compared to the former sets, for complete information extraction. In
fact, this difference in the number of required entangled states for complete
information extraction grows linearly with the number of parties. This study
sheds light on suitable use of local indistinguishability property of quantum
states as resource and thus, we demonstrate an efficient way of information
distribution.
