Nonlocal sets of orthogonal multipartite product states with less members

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 ${\mathcal{C}}^d\otimes {\mathcal{C}}^d\otimes {\mathcal{C}}^d(d\ge 3)$ and ${\mathcal{C}}^d\otimes {\mathcal{C}}^{d+1}\otimes {\mathcal{C}}^{d+2}(d\ge 3)$. Then for general tripartite quantum system ${\mathcal{C}}^{n_1}\otimes {\mathcal{C}}^{n_2}\otimes {\mathcal{C}}^{n_3}$ $(3\le n_1\le n_2\le n_3)$, we obtain $2(n_2+n_3-1)-n_1$ nonlocal orthogonal product states. Finally, we put forward a new construction approach in ${\mathcal{C}}^{d_1}\otimes {\mathcal{C}}^{d_2}\otimes \cdots \otimes {\mathcal{C}}^{d_n}$ $(d_1,d_2,\cdots d_n\ge 3,n>6)$ 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.

15 pages

References in corpus (4)

• Multipartite Nonlocality without Entanglement in Many Dimensions
• Quantum secret sharing based on local distinguishability
• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
• Detecting the local indistinguishability of maximally entangled states