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arXiv · 2303.15001

Quantum $k$-uniform states from quantum orthogonal arrays

Yajuan Zang·Zihong Tian·Shao-Ming Fei·Hui-Juan Zuo
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Abstract

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of $N$ systems with dimension of prime power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform states of $N$-qubit systems for arbitrary $N\geq 6$ and $N\neq 7,8,9,11$; 3-uniform states of $N$ systems with dimension of prime power $d\geq 7$ for arbitrary $N\geq 7$.

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Yajuan Zang, Zihong Tian, Shao-Ming Fei, Hui-Juan Zuo. 2023-03-27. Quantum $k$-uniform states from quantum orthogonal arrays. https://doi.org/10.1007/s10773-023-05316-w

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