Over the past two decades, much progress has been made in the construction of nonlocal sets without entanglement. In 2023, Li and Wang proposed an open question that an orthogonal product set (OPS) $\mathcal{S}$ is locally stable with minimum cardinality in general multipartite systems and the numerical lower bound for such a set was given by Wang {\it et al.}, $(\left| \mathcal{S} \right |-1)\left| \mathcal{S} \right | \geq \sum_{i=1}^{n}(d_{i}^2-1)$, but the existence of the construction remains unresolved.

In this talk, I will introduce the method that construct locally stable sets with minimum cardinalities $d^2$ and $d^2+1$ via $1$-orthogonal cyclic product sets in $(\mathbb{C}^{d})^ {\otimes d^2}$ for odd $d$ and $(\mathbb{C}^{d})^{\otimes d^2+1}$ for even $d$. Furthermore, I will present locally stable OPSs with smaller size in general multipartite systems.

甄晓帆，北京邮电大学博士研究生，导师为高飞教授，研究方向为量子信息与量子计算。