Nonlocal sets of orthogonal multipartite product states with less members

• Published in: Quantum information processing Vol. 20; no. 12
• Main Authors: Zuo, Hui-Juan, Liu, Jia-Huan, Zhen, Xiao-Fan, Fei, Shao-Ming
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2021; Springer Nature B.V
• Subjects: Data processing; Data Structures and Information Theory; Mathematical Physics; Physics; Physics and Astronomy; Quantum Computing; Quantum Information Technology; Quantum phenomena; Quantum Physics; Quantum theory; Spintronics; local operations and classical communication; local indistinguishability; Nonlocal set; orthogonal product state
• ISSN: 1570-0755; 1573-1332
• DOI: 10.1007/s11128-021-03320-9

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 C d ⊗ C d ⊗ C d ( d ≥ 3 ) and C d ⊗ C d + 1 ⊗ C d + 2 ( d ≥ 3 ) . Then for general tripartite quantum system C n 1 ⊗ C n 2 ⊗ C n 3 ( 3 ≤ n 1 ≤ n 2 ≤ 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 C d 1 ⊗ C d 2 ⊗ ⋯ ⊗ C d n ( d 1 , d 2 , ⋯ d n ≥ 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.