Nonlocal sets of orthogonal multipartite product states with less members

• URL: http://arxiv.org/abs/2111.09770v1
• Date: Thu, 18 Nov 2021 16:05:31 GMT
• Title: Nonlocal sets of orthogonal multipartite product states with less members
• Authors: Hui-Juan Zuo, Jia-Huan Liu, Xiao-Fan Zhen, Shao-Ming Fei
• Abstract summary: We study the constructions of nonlocal product states in multipartite systems that cannot be distinguished by local operations and classical communication. Remarkably, our sets contain less nonlocal product states than the existing ones, which improves the recent results and highlights their related applications in quantum information processing.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the constructions of nonlocal orthogonal product states in multipartite systems that cannot be distinguished by local operations and classical communication. We first present two constructions of nonlocal orthogonal product states in tripartite systems $\mathcal{C}^{d}\otimes\mathcal{C}^{d}\otimes\mathcal{C}^{d}~(d\geq3)$ and $\mathcal{C}^d\otimes \mathcal{C}^{d+1}\otimes \mathcal{C}^{d+2}~(d\geq 3)$. Then for general tripartite quantum system $\mathcal{C}^{n_{1}}\otimes\mathcal{C}^{n_{2}}\otimes\mathcal{C}^{n_{3}}$ $(3\leq n_{1}\leq n_{2}\leq n_{3})$, we obtain $2(n_{2}+n_{3}-1)-n_{1}$ nonlocal orthogonal product states. Finally, we put forward a new construction approach in $\mathcal{C}^{d_{1}}\otimes \mathcal{C}^{d_{2}}\otimes\cdots\otimes \mathcal{C}^{d_{n}}$ $(d_1,d_2,\cdots d_n\geq3,\, n>6)$ multipartite systems. Remarkably, our indistinguishable sets contain less nonlocal product states than the existing ones, which improves the recent results and highlights their related applications in quantum information processing.

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