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arXiv · 2006.04086

Constructions of $k$-uniform states from mixed orthogonal arrays

Fei Shi·Yi Shen·Lin Chen·Xiande Zhang
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Abstract

We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. Based on the connections between mixed orthogonal arrays with certain minimum Hamming distance, irredundant mixed orthogonal arrays and $k$-uniform states, we present two constructions of $2$-uniform states in heterogeneous systems. We also construct a family of $3$-uniform states in heterogeneous systems, which solves a question posed in [D. Goyeneche et al., Phys. Rev. A 94, 012346 (2016)]. We also show two methods of generating $(k-1)$-uniform states from $k$-uniform states. Some new results on the existence and nonexistence of absolutely maximally entangled states are provided. For the applications, we present an orthogonal basis consisting of $k$-uniform states with minimum support. Moreover, we show that some $k$-uniform bases can not be distinguished by local operations and classical communications, and this shows quantum nonlocality with entanglement.

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Fei Shi, Yi Shen, Lin Chen, Xiande Zhang. 2020-06-07. Constructions of $k$-uniform states from mixed orthogonal arrays. https://arxiv.org/abs/2006.04086

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