Unextendible and uncompletable product bases in every bipartition
arXiv:2207.04763 · doi:10.1088/1367-2630/ac9e14
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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- Genuinely nonlocal sets without entanglement in multipartite systems
- Unextendible and strongly uncompletable product bases
- Progress in the study of the (non)existence of genuinely unextendible product bases