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

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 $n\ge m\ge 3$. 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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Cited by in corpus (11)

• Strong quantum nonlocality with entanglement
• Strongly nonlocal unextendible product bases do exist
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Unextendible product bases, bound entangled states, and the range criterion
• Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
• Unextendible and uncompletable product bases in every bipartition
• Strong quantum nonlocality from hypercubes
• Negative result about the construction of genuinely entangled subspaces from unextendible product bases
• Unextendible product operator basis
• Unextendible and strongly uncompletable product bases
• Constructing unextendible product bases from multiqubit ones