2020/03/16 by Guang‐Bao Xu, G. B. Xu, D. H. Jiang +3
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Chemistry #Combinatorics #Computer science #Construct (python library) #Crystallography #Discrete mathematics #FOS: Physical sciences #Geometry #Isomorphism (crystallography) #Mathematics #Physics #Product (mathematics) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum mechanics #Quantum optics and atomic interactions #Set (abstract data type) #Work (physics) #quant-ph
paper · pdf · doi:10.48550/arxiv.2003.08291
arXiv admin note: text overlap with arXiv:2003.06852
openalex publication_date 2020/03/16 · openalex created_date 2020/03/23 · arxiv created 2020/07/28 · arxiv updated 2020/07/29 · openalex updated_date 2026/08/06
Nonlocal sets of orthogonal product states (OPSs) are widely used in quantum protocols owing to their good property. Thus a lot of attention are paid to how to construct a nonlocal set of orthogonal product states though it is a difficult problem. In this paper, we propose a novel general method to construct a nonlocal set of orthogonal product states in ℂd ⊗ ℂd for d≥3. We give an ingenious proof for the local indistinguishability of those product states. The set of product states, which are constructed by our method, has a very good structure. Subsequently, we give a construction of nonlocal set of OPSs with smaller members in ℂd ⊗ ℂd for d≥3. On the other hand, we present two construction methods of nonlocal sets of OPSs in ℂm ⊗ ℂn, where m≥3 and n≥3. Furthermore, we propose the concept of isomorphism for two nonlocal sets of OPSs. Our work is of great help to understand the structure and classification of locally indistinguishable OPSs.