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 compact localized states.
A Complete Characterization of Pretty Good State Transfer on Paths
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abstract
We give a complete characterization of pretty good state transfer on paths between any pair of vertices with respect to the quantum walk model determined by the XY-Hamiltonian. If $n$ is the length of the path, and the vertices are indexed by the positive integers from 1 to $n$, with adjacent vertices having consecutive indices, then the necessary and sufficient conditions for pretty good state transfer between vertices $a$ and $b$ are that (a) $a + b = n + 1$, (b) $n + 1$ has at most one odd non-trivial divisor, and (c) if $n = 2^t r - 1$, for $r$ odd and $r \neq 1$, then $a$ is a multiple of $2^{t - 1}$.
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quant-ph 1years
2019 1verdicts
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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 compact localized states.