Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
We completely characterize the condition when a tile structure provides an unextendible product basis (UPB), and construct UPBs of different large sizes in $\mathbb{C}^m\otimes\mathbb{C}^n$ for any $n\geq m\geq 3$. This solves an open problem in [S. Halder et al., Phys. Rev. A 99, 062329 (2019)]. As an application, we show …