Isomorphism of nonlocal sets of orthogonal product states in bipartite quantum systems

Guang-Bao Xu, Yan-Ying Zhu, Dong-Huan Jiang and Yu-Guang Yang

Physica A: Statistical Mechanics and its Applications, 2023, vol. 619, issue C

Abstract: To characterize nonlocal sets of orthogonal product states (OPSs) in a given bipartite quantum system, we propose two new concepts, i.e., orthogonal relation matrix of a set of OPSs and isomorphism of different sets of OPSs. In ℂ3⊗ℂ3 quantum system, we find that two sets of OPSs, which are isomorphic to a nonlocal set of OPSs, are locally indistinguishable. In ℂ5⊗ℂ5 quantum system, we construct a new nonlocal set of OPSs according to the orthogonal relation matrix of a set of OPSs that cannot be perfectly distinguished by local operations and classical communication (LOCC). These results show a phenomenon that a set of OPSs is locally indistinguishable if its orthogonal relation matrix is equivalent to the orthogonal relation matrix of another set of OPSs that cannot be perfectly distinguished by LOCC in a given quantum system, and the orthogonal relation matrix of a nonlocal set of OPSs can be used to construct a new nonlocal set of OPSs. On the other hand, we give the geometric interpretation of nonlocal sets with isomorphism relation by orthogonal graphs (OGs). Our results, which can be used to classify nonlocal sets of bipartite OPSs, improve the theory of local distinguishability and deepen people’s understanding of the structures of nonlocal sets.

Keywords: Quantum nonlocality without entanglement; Orthogonal product state; Orthogonal relation matrix; Isomorphism (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437123002893
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:619:y:2023:i:c:s0378437123002893

DOI: 10.1016/j.physa.2023.128734

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().