Strong quantum nonlocality with genuine entanglement in an $N$-qutrit system

• DOI: 10.48550/arxiv.2308.16409
• Publication Date: 2023-01-01
• Authors: Mengying Hu; Ting Gao; Fengli Yan
• Keywords: Qutrit; Multipartite; Greenberger–Horne–Zeilinger state

In this paper, we construct genuinely multipartite entangled bases in $(\mathbb{C}^{3})^{\otimes N}$ for $N\geq3$, where every state is one-uniform state. By modifying construction, successfully obtain strongly nonlocal orthogonal sets and bases, which provide an answer to the open problem raised by Halder $et~al.$ [\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.040403} {Phy. Rev. Lett. \textbf{122}, 040403 (2019)}]. The genuine set constructed contains much fewer quantum states than all known ones. When $N>3$, our result answers question given Wang $et~al$. [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.012424} {Phys. A \textbf{104}, 012424 (2021)}].