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

TL;DR

This paper constructs strongly nonlocal, genuinely entangled bases in multi-qutrit systems, providing solutions to open problems in quantum nonlocality and entanglement with fewer states than previous methods.

Contribution

It introduces a novel construction of genuinely multipartite entangled bases and strongly nonlocal sets in N-qutrit systems, addressing open questions in quantum nonlocality.

Findings

Constructed genuinely entangled bases in N-qutrit systems.

Developed strongly nonlocal orthogonal entangled sets and bases.

Achieved more efficient entangled sets with fewer states than existing ones.

Abstract

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 this construction, we successfully obtain strongly nonlocal orthogonal genuinely entangled sets and strongly nonlocal orthogonal genuinely entangled 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 strongly nonlocal orthogonal genuine entangled set we constructed in $(\mathbb{C}^{3})^{\otimes N}$ contains much fewer quantum states than all known ones. When $N>3$, our result answers the open question given by Wang $et~al$. [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.012424} {Phys. Rev. A \textbf{104}, 012424 (2021)}].