在每一个二分区中不可扩展和不可完成的产品基础
Unextendible and uncompletable product bases in every bipartition
摘要：
不可拓积基是量子信息理论中的一个重要研究对象，具有广泛的应用前景，包括束缚纠缠态、无纠缠的量子非定域性、无量子破坏的贝尔不等式等。一个广义的概念称为不完全乘积基也引起了人们的广泛关注。在本文中，我们发现了一些不可扩张的乘积基，它们在每一个双划分中都是不可完全的乘积基，这回答了Dienizo等人提出的一个19年前的公开问题。Math.Phys.238，379（2003）]。因此，我们将这种不可扩张乘积基与信息的局部隐藏联系起来，并给出了不可扩张乘积基存在的充分条件，即在每一个双划分中，不可扩张乘积基仍然是不可扩张乘积基。我们的研究结果推进的几何形状的不可扩展的产品基地的理解。
英文摘要：
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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