Small set of orthogonal product states with nonlocality

A set of orthogonal states in multipartite systems is called to be locally stable if preserve the orthogonality states, only trivial local measurement can performed for each partite. Locally sets are always indistinguishable yielding a form nonlocality which different from Bell-type nonlocality. In this work, we study product with small size. First, give lower bound on size states. It well known that unextendible basis (UPB) indistinguishable. But find some them not stable. On other hand, there exists subsets minimum UPB also implies such UPBs stronger than form.