Strong quantum nonlocality in N -partite systems

A set of multipartite orthogonal quantum states is strongly nonlocal if it is locally irreducible for every bipartition of the subsystems [S. Halder, M. Banik, S. Agrawal, and S. Bandyopadhyay, Phys. Rev. Lett. 122, 040403 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.040403]. Although this property has been shown in three-, four-, and five-partite systems, the existence of strongly nonlocal sets in N-partite systems remains unknown when N=6. In this paper, we successfully show that a strongly nonlocal set of orthogonal entangled states exists in (Cd) - N for all N=3 and d=2, which reveals the strong quantum nonlocality in general N-partite systems. For N=3 or 4 and d=3, we present a strongly nonlocal set consisting of genuinely entangled states, which has a smaller size than any known strongly nonlocal orthogonal product set. Finally, we connect strong quantum nonlocality with local hiding of information as an application.