Unextendible and uncompletable product bases in every bipartition

Abstract Unextendible product basis is an important object in quantum information theory and features a broad spectrum of applications, ranging from quantum nonlocality to quantum cryptography. A generalized concept called uncompletable product basis also attracts much attention. In this paper, we f...

Full description

Saved in:
Bibliographic Details
Published inNew journal of physics Vol. 24; no. 11; pp. 113025 - 113041
Main Authors Shi, Fei, Li, Mao-Sheng, Zhang, Xiande, Zhao, Qi
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.11.2022
Subjects
Communication
Entangled states
Hilbert space
Information theory
Physics
Quantum cryptography
Quantum entanglement
Quantum phenomena
Quantum theory
Questions
tile structures
uncompletable product bases
unextendible product bases
Online AccessGet full text

Cover

More Information
Summary:Abstract Unextendible product basis is an important object in quantum information theory and features a broad spectrum of applications, ranging from quantum nonlocality to quantum cryptography. A generalized concept called uncompletable product basis also attracts much attention. In this paper, we find some unextendible product bases that are uncompletable product bases in every bipartition, which answers a 19 year-old open question proposed by DiVincenzo et al (2003 Commun. Math. Phys. 238 379–410). As a consequence, we connect such unextendible product bases to local hiding of information, positive-partial-transpose entangled states and genuinely entangled states. Furthermore, we give a sufficient condition for the existence of an unextendible product basis that is still unextendible in every bipartition, and the existence of such a UPB is another open question proposed by Demianowic et al (2018 Phys. Rev. A 98 012313). Our results advance the understanding of the geometry of unextendible product bases.
Bibliography:NJP-115269.R1
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ac9e14