Local indistinguishability: more nonlocality with less entanglement

We provide a first operational method for checking indistinguishability of orthogonal states by local operations and classical communication (LOCC). This method originates from the one introduced by Ghosh et al. (Phys. Rev. Lett. 87, 5807 (2001) (quant-ph/0106148)), though we deal with pure states. We apply our method to show that an arbitrary complete multipartite orthogonal basis is indistinguishable by LOCC, if it contains at least one entangled state. We also show that probabilistic local distinguishing is possible for full basis if and only if all vectors are product. We employ our method to prove local indistinguishability in an example with sets of pure states of 3X3, which shows that one can have ``more nonlocality with less entanglement'', where ``more nonlocality'' is in the sense of ``increased local indistinguishability of orthogonal states''. This example also provides, to our knowledge, the only known example where d orthogonal states in dXd are locally indistinguishable.