论文标题
来自瓷砖结构及其本地纠缠辅助的区分性的不可避免的产品库
Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
论文作者
论文摘要
当瓷砖结构提供不可扩展的产品基础（UPB）并在$ \ Mathbb {C}^M \ otimes \ Mathbb {C}^n $中构建不同尺寸的UPB时，我们完全表征了条件。这解决了[S. Halder等人，物理。 Rev. A 99，062329（2019）]。作为一个应用程序，我们表明我们的大小$（Mn-4 \ lfloor \ frac {m-1} {2} {2} \ rfloor）$ in $ \ m \ mthbb {c}^m \ otimes \ mathbb {c}^n $可以由本地操作和经典沟通辅助区分$ \ lceil \ frac {m} {2} \ rceil \ otimes \ lceil \ frac {m} {2} {2} \ rceil $最大纠缠状态。
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 that our UPBs of size $(mn-4\lfloor\frac{m-1}{2}\rfloor)$ in $\mathbb{C}^m\otimes\mathbb{C}^n$ 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.
