A Complete Characterization of Pretty Good State Transfer on Paths

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 $r\ne 1$, then $a$ is a multiple of $2^{t-1}$.

9 pages (v1); 8 pages (v2), minor edits and updates

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• Universal computation by quantum walk
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Cited by in corpus (2)

• Designing pretty good state transfer via isospectral reductions
• Data classification by quantum radial basis function networks