Strongly nonlocal unextendible product bases do exist

• URL: http://arxiv.org/abs/2101.00735v3
• Date: Sat, 1 Jan 2022 01:05:09 GMT
• Title: Strongly nonlocal unextendible product bases do exist
• Authors: Fei Shi, Mao-Sheng Li, Mengyao Hu, Lin Chen, Man-Hong Yung, Yan-Ling Wang, Xiande Zhang
• Abstract summary: We show the existence of unextendible product bases (UPBs) that are locally irreducible. These UPBs exhibit the phenomenon of strong quantum nonlocality without entanglement. It sheds new light on the connections between UPBs and strong quantum nonlocality.
• Score: 14.686974497801048
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective way to prove that a set is locally irreducible is to show that only trivial orthogonality-preserving local measurement can be performed to this set. In general, it is difficult to show that such an orthogonality-preserving local measurement must be trivial. In this work, we develop two basic techniques to deal with this problem. Using these techniques, we successfully show the existence of unextendible product bases (UPBs) that are locally irreducible in every bipartition in $d\otimes d\otimes d$ for any $d\geq 3$, and $3\otimes3\otimes 3$ achieves the minimum dimension for the existence of such UPBs. These UPBs exhibit the phenomenon of strong quantum nonlocality without entanglement. Our result solves an open question given by Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] and Yuan \emph{et al.} [Phys. Rev. A \textbf{102}, 042228 (2020)]. It also sheds new light on the connections between UPBs and strong quantum nonlocality.

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