  Quantum nonlocality has different manifestations that, in general, are
revealed by local measurements of the parts of a composite system. In this
paper, we study nonlocality arising from a set of orthogonal states that cannot
be perfectly distinguished by local operations and classical communication
(LOCC). Such a set is deemed nonlocal, for a joint measurement on the whole
system is necessary for perfect discrimination of the states with certainty. On
the other hand, a set of orthogonal states that can be perfectly distinguished
by LOCC is believed to be devoid of nonlocal properties. Here, we show that
there exist orthogonal sets that are locally distinguishable but without local
redundancy (i.e., they become nonorthogonal on discarding one or more
subsystems) whose nonlocality can be activated by local measurements. In
particular, a state chosen from such a set can be locally converted, with
certainty, into another state, the identity of which can now only be
ascertained by global measurement and no longer by LOCC. In other words, a
locally distinguishable set without local redundancy may be locally converted
into a locally indistinguishable set with certainty. We also suggest an
application, namely, local hiding of information, that allows us to locally
hide locally available information without losing any part. Once hidden, the
information in its entirety can only be retrieved using entanglement.
