Nonlocal sets of orthogonal multipartite product states with less members

TL;DR

This paper constructs smaller sets of nonlocal orthogonal product states in multipartite quantum systems, demonstrating their indistinguishability by local operations, which advances understanding of quantum nonlocality with fewer resources.

Contribution

The paper introduces new methods to construct nonlocal orthogonal product states with fewer members than previous approaches in multipartite systems.

Findings

Constructed nonlocal orthogonal product states in tripartite systems.

Derived a formula for the number of nonlocal states in general tripartite systems.

Presented a new construction approach for multipartite systems with more than six parties.

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.