Fractional revival on quasi-abelian Cayley graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917930708500480 |
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| author | Fang, Yi Huang, Xueyi Liu, Xiaogang Zhan, Xiongfeng |
| author_facet | Fang, Yi Huang, Xueyi Liu, Xiaogang Zhan, Xiongfeng |
| contents | Fractional revival, a quantum transport phenomenon critical to entanglement generation in quantum spin networks, generalizes the notion of perfect state transfer on graphs. A Cayley graph $\mathrm{Cay}(G,S)$ is called quasi-abelian if its connection set $S$ is a union of conjugacy classes of the group $G$. In this paper, we establish a necessary and sufficient condition for quasi-abelian Cayley graphs to have fractional revival. This extends a result of Cao and Luo (2022) on the existence of fractional revival in Cayley graphs over abelian groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_14330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional revival on quasi-abelian Cayley graphs Fang, Yi Huang, Xueyi Liu, Xiaogang Zhan, Xiongfeng Combinatorics 05C50, 81P68 Fractional revival, a quantum transport phenomenon critical to entanglement generation in quantum spin networks, generalizes the notion of perfect state transfer on graphs. A Cayley graph $\mathrm{Cay}(G,S)$ is called quasi-abelian if its connection set $S$ is a union of conjugacy classes of the group $G$. In this paper, we establish a necessary and sufficient condition for quasi-abelian Cayley graphs to have fractional revival. This extends a result of Cao and Luo (2022) on the existence of fractional revival in Cayley graphs over abelian groups. |
| title | Fractional revival on quasi-abelian Cayley graphs |
| topic | Combinatorics 05C50, 81P68 |
| url | https://arxiv.org/abs/2502.14330 |