Abstract
Local distinguishability of orthogonal product states is an area of active research in quantum information theory. However, most of the relevant results about local distinguishability are found in bipartite quantum systems and very few are known in multipartite cases. In this paper, we construct a locally indistinguishable subset in $${\mathbb {C}}^{2d}\bigotimes {\mathbb {C}}^{2d}\bigotimes {\mathbb {C}}^{2d}$$ , $$d\ge 2$$ that contains $$18(d-1)$$ orthogonal product states. Further, we generalize our method to arbitrary tripartite quantum systems $${\mathbb {C}}^{k}\bigotimes {\mathbb {C}}^{l}\bigotimes {\mathbb {C}}^{m}$$ . This result helps us to understand the role of nonlocality without entanglement in multipartite quantum systems. Finally, we prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states.
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