  The principle of local distinguishability states that an arbitrary physical
state of a bipartite system can be determined by the combined statistics of
local measurements performed on the subsystems. A necessary and sufficient
requirement for the local measurements is that each one must be able to
distinguish between all pairs of states of the respective subsystems. We show
that if the task is changed into the determination of an arbitrary bipartite
pure state, then at least in certain cases it is possible to restrict to local
measurements which can distintinguish all pure states but not all states. This
surprising fact gives evidence that the principle of local distinguishability
may be expanded beyond its usual applicability.
