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arXiv · 2605.00518

Quantum fractional revival on zero-divisor graphs over $\mathbb{Z}_n$

Bui Phuoc Minh·Songpon Sriwongsa
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Abstract

In this paper, we characterize the existence of perfect state transfer (PST) and fractional revival in continuous-time quantum walks on the zero-divisor graph $\Gamma(\mathbb{Z}_n)$. By using the canonical equitable partition of $\Gamma(\mathbb{Z}_n)$ induced by the proper divisors of $n$, we derive a sufficient condition on $n$ for PST to occur between a pair of vertices. We show that fractional revival is restricted to cells of size $2$ within the equitable partition. Furthermore, assuming $-1$ is not an eigenvalue of the quotient spectrum, we establish that two vertices in $\Gamma(\mathbb{Z}_n)$ are strongly cospectral if and only if they form a cell of size $2$ within the equitable partition that is either a set of false twins or true twins. Finally, we provide a characterization of fractional revival on bipartite $\Gamma(\mathbb{Z}_n)$ and prove the non-existence of fractional revival on $\Gamma(\mathbb{Z}_{p^2q})$.

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Bui Phuoc Minh, Songpon Sriwongsa. 2026-05-01. Quantum fractional revival on zero-divisor graphs over $\mathbb{Z}_n$. https://arxiv.org/abs/2605.00518

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