Unextendible and uncompletable product bases in every bipartition

• URL: http://arxiv.org/abs/2207.04763v1
• Date: Mon, 11 Jul 2022 10:49:34 GMT
• Title: Unextendible and uncompletable product bases in every bipartition
• Authors: Fei Shi, Mao-Sheng Li, Xiande Zhang, and Qi Zhao
• Abstract summary: Unextendible product basis is an important object in quantum information theory. We find some unextendible product bases that are uncompletable product bases in every bipartition. Our results advance the understanding of the geometry of unextendible product bases.
• Score: 23.76183357793457
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Unextendible product basis is an important object in quantum information theory and features a broad spectrum of applications, ranging bound entangled states, quantum nonlocality without entanglement, and Bell inequalities with no quantum violation. 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. [Commun. Math. Phys. 238, 379 (2003)]. As a consequence, we connect such unextendible product bases to local hiding of information and give a sufficient condition for the existence of an unextendible product basis, that is still an unextendible product basis in every bipartition. Our results advance the understanding of the geometry of unextendible product bases.

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