Local indistinguishability and LOCC monotones

Details Local indistinguishability and LOCC monotones Local indistinguishability and LOCC monotones

2002-04-19

arxiv.org/abs/quant-ph/0204116v2

Physics

Quantum Physics

9 pages, LaTeX, no figures

Scientific paper

We provide a method for checking indistinguishability of a set of multipartite orthogonal states by local operations and classical communication (LOCC). It bases on the principle of nonincreasing of entanglement under LOCC. This method originates from the one introduced by Ghosh \emph{et al.} (Phys. Rev. Lett. \textbf{87}, 5807 (2001) (quant-ph/0106148)), though we deal with {\emph pure} states. In the bipartite case, our method is operational, although we do not know whether it can always detect local indistinguishability. We apply our method to show that an arbitrary complete multipartite orthogonal basis is indistinguishable if it contains at least one entangled state. We also show that probabilistic distinguishing is possible for full basis if and only if all vectors are product. We employ our method to prove local indistinguishability in a very interesting example akin to "nonlocality without entanglement".

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