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An orthogonal product basis of a composite Hilbert space is genuinelynonlocal if the basis states are locally indistinguishable across everybipartition. From an operational point of view such a basis corresponds to aseparable measurement that cannot be implemented by local operations andclassical communication (LOCC) unless all the parties come together in a singlelocation. In this work we classify genuinely nonlocal product bases intodifferent categories. Our classification is based on state elimination propertyof the set via orthogonality-preserving measurements when all the parties arespatially separated or different subsets of the parties come together. We thenstudy local state discrimination protocols for several such bases withadditional entangled resources shared among the parties. Apart from consumingless entanglement than teleportation based schemes our protocols indicateoperational significance of the proposed classification and exhibit nontrivialuse of genuine entanglement in local state discrimination problem.

Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination