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Fractional revival on abelian Cayley graphs
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Fractional revival, known as a quantum transport phenomenon, is essential for entanglement generation in quantum spin networks. The concept of fractional revival is a generalization of perfect state transfer and periodicity on graphs. In this paper, we propose a sufficient and necessary condition for abelian Cayley graphs having fractional revival between any two distinct vertices. With this characterization, two general constructions of abelian Cayley graphs having fractional revival is presented. Meanwhile, we establish several new families of abelian Cayley graphs admitting fractional revival.
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State Transfer on Unitary Cayley Graphs and Quadratic Unitary Cayley Graphs
Unitary Cayley graphs admit pretty good fractional revival and fractional revival exactly when the vertex count is 2 or twice a prime; quadratic unitary Cayley graphs admit pretty good fractional revival exactly for c...
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