Fractional revival between twin vertices

Monterde, Hermie

doi:10.1016/j.laa.2023.07.006

Cited by 2 publications

(1 citation statement)

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“…Thus, blow-ups have the advantage of producing pairs of vertices that are promising for high probability state transfer. Lastly, the two copies of a vertex in G are twins in 2 ⊎ G. This allows us to utilize some of the recent work on quantum state transfer between twins [KMP23,Mon23a,Pal22]. In particular, we give characterizations of strong cospectrality, PST, PGST and periodicity in blow-up graphs (see theorems 2-5).…”

Section: Introductionmentioning

confidence: 99%

Quantum walks on blow-up graphs

Bhattacharjya,

Monterde,

Pal

2024

J. Phys. A: Math. Theor.

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A blow-up of n copies of a graph G is the graph obtained by replacing every vertex of G by an independent set of size n, where the copies of two vertices in G are adjacent in the blow-up if and only if the two vertices are adjacent in G. In this work, we characterize strong cospectrality, periodicity, perfect state transfer (PST) and pretty good state transfer (PGST) in blow-up graphs. We prove that if a blow-up graph admits PST or PGST, then n=2. In particular, if G has an invertible adjacency matrix, then each vertex in a blow of two copies of G pairs up with a unique vertex to exhibit strong cospectrality. Under mild conditions, we show that periodicity (resp., almost periodicity) of a vertex in G guarantees PST (resp. PGST) between the two copies of the vertex in the blow-up. Moreover, we characterize PST and PGST in blow-ups of complete graphs, paths, cycles and cones. Finally, while trees in general do not admit PST, we provide infinite families of stars and subdivided stars whose blow-ups admit PST.

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Section: Introductionmentioning

confidence: 99%