2020/03/15 by D. H. Jiang, Dong‐Huan Jiang, Guang‐Bao Xu +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Constraint (computer-aided design) #Discrete mathematics #Geometry #Mathematics #Multipartite #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum entanglement #Quantum mechanics #Quantum state #Set (abstract data type) #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.1103/physreva.102.032211
published as Phys. Rev. A 102, 032211 (2020)
arxiv created 2020/03/15 · openalex publication_date 2020/09/10 · arxiv updated 2020/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recently, much attention have been paid to the constructions of nonlocal multipartite orthogonal product states. Among the existing results, some are relatively complex in structure while others have many constraint conditions. In this paper, we first give a simple method to construct a nonlocal set of orthogonal product states in \ensuremath\bigotimesj=1nℂd, where d,\phantom\rule0.16em0exn are two positive integers, d\ensuremath≥2 and n\ensuremath≥3. Then we give a proof for local indistinguishability of the set constructed by our method. According to the characteristics of this construction method, we get a new construction of nonlocal set with fewer states in the same quantum system. Furthermore, we generalize these two results to a more general \ensuremath\bigotimesj=1nℂ^dj quantum system, where n,\phantom\rule0.16em0exdj are two positive integers, n\ensuremath≥3 and dj\ensuremath≥2. Compared with the existing results, the nonlocal set of multipartite orthogonal product states constructed by our method has fewer elements and is simpler. Most of all, our multipartite constructions are more general than the ones reported earlier.