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

• URL: http://arxiv.org/abs/2006.04086v1
• Date: Sun, 7 Jun 2020 08:35:22 GMT
• Title: Constructions of $k$-uniform states from mixed orthogonal arrays
• Authors: Fei Shi, Yi Shen, Lin Chen, Xiande Zhang
• Abstract summary: We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. We present two constructions of $2$-uniform states in heterogeneous systems. We show that some $k$-uniform bases can not be distinguished by local operations and classical communications.
• Score: 18.378398718548016
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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