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Pretty good state transfer between internal nodes of paths
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abstract
We study a continous-time quantum walk on a path graph. In this paper, we show that, for any odd prime $p$ and positive integer $t$, the path on $2^t p - 1$ vertices admits pretty good state transfer between vertices $a$ and $n+1-a$ for each $a$ that is a multiple of $2^{t-1}$ with respect to the quantum walk model determined by the XY-Hamiltonian. This gives the first examples of pretty good state transfer occurring between internal vertices on a path, when it does not occur between the extremal vertices.
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Cited by 1 Pith paper
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Designing pretty good state transfer via isospectral reductions
An algorithm uses isospectral reductions to extract the polynomial factors that guarantee pretty good state transfer, then tunes network parameters to satisfy them, with an extension to storing and transferring compac...
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