Tile structures for unextendible product bases

Fei Shi, Xiande Zhang, Lin Chen

Published 2020-03-09Version 1

We construct the notions of tile and U-tile structures. A tile structure corresponds to an $m\times n$ unextendible product basis (UPB) if and only if it is a U-tile structure. We construct UPBs of large size in terms of the U-tile structures. In particular we solve an open problem in [S. Halder et al., Phys. Rev. A 99, 062329 (2019)]. As an application, we show that some UPBs can be perfectly distinguished by local operations and classical communications assisted with a $\lceil\frac{m}{2}\rceil\otimes\lceil\frac{m}{2}\rceil$ maximally entangled state.