Strong quantum nonlocality in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> -partite systems

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