Novel Constructions of Mutually Unbiased Tripartite Absolutely Maximally Entangled Bases

• URL: http://arxiv.org/abs/2209.08462v1
• Date: Sun, 18 Sep 2022 03:42:20 GMT
• Title: Novel Constructions of Mutually Unbiased Tripartite Absolutely Maximally Entangled Bases
• Authors: Tian Xie, Yajuan Zang, Hui-Juan Zuo, Shao-Ming Fei
• Abstract summary: We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in $mathbbCd otimes mathbbCd$ We then generalize the approach to the case of $mathbbCd_1 otimes mathbbCd_2 otimes mathbbCd_1d_1d_2$ by mutually weak Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are
• Score: 1.8065361710947974
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in $\mathbb{C}^{d} \otimes \mathbb{C}^{d} \otimes \mathbb{C}^{d}$ based on mutually orthogonal Latin squares. Then we generalize the approach to the case of $\mathbb{C}^{d_{1}} \otimes \mathbb{C}^{d_{2}} \otimes \mathbb{C}^{d_{1}d_{2}}$ by mutually weak orthogonal Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Detailed examples in $\mathbb{C}^{3} \otimes \mathbb{C}^{3} \otimes \mathbb{C}^{3},$ $\mathbb{C}^{2} \otimes \mathbb{C}^{2} \otimes \mathbb{C}^{4}$ and $\mathbb{C}^{2} \otimes \mathbb{C}^{5} \otimes \mathbb{C}^{10}$ are provided to illustrate the advantages of our approach.

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