Quantum $k$-uniform states from quantum orthogonal arrays

• URL: http://arxiv.org/abs/2303.15001v1
• Date: Mon, 27 Mar 2023 08:43:35 GMT
• Title: Quantum $k$-uniform states from quantum orthogonal arrays
• Authors: Yajuan Zang, Zihong Tian, Shao-Ming Fei, Hui-Juan Zuo
• Abstract summary: We give infinite classes of 2-uniform states of $N$ systems with dimension of prime power $dgeq 2$ for arbitrary $Ngeq 5$. We also give 3-uniform states of $N$-qubit systems for arbitrary $Ngeq 6$ and $Nneq 7,8,9,11$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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