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Recently, Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)]proposed the concept strong nonlocality without entanglement: an orthogonal setof fully product states in multipartite quantum systems that is locallyirreducible for every bipartition of the subsystems. As the difficulty of theproblem, most of the results are restricted to tripartite systems. Here weconsider a weaker form of nonlocality called local distinguishability basedgenuine nonlocality. A set of orthogonal multipartite quantum states is said tobe genuinely nonlocal if it is locally indistinguishable for every bipartitionof the subsystems. In this work, we tend to study the latter form ofnonlocality. First, we present an elegant set of product states in bipartitesystems that is locally indistinguishable. After that, based on a simpleobservation, we present a general method to construct genuinely nonlocal setsof multipartite product states by using those sets that are genuinely nonlocalbut with less parties. As a consequence, we obtain that genuinely nonlocal setsof fully product states exist for all possible multipartite quantum systems.

Local distinguishability based genuinely quantum nonlocality without entanglement