Unextendible product bases from tile structures and their local entanglement-assisted distinguishability

• URL: http://arxiv.org/abs/2003.03898v2
• Date: Mon, 23 Mar 2020 02:52:32 GMT
• Title: Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
• Authors: Fei Shi, Xiande Zhang, and Lin Chen
• Abstract summary: We characterize the condition when a tile structure provides an unextendible product basis (UPB) We show that our UPBs of size $(mn-4lfloorfracm-12rfloor)$ in $mathbbCmotimesmathbbCn$ can be perfectly distinguished by local operations and classical communications.
• Score: 16.424004426651326
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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