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Quantum Information Processing

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01-07-2023 | Regular Article

Sedentariness in quantum walks

Author: Hermie Monterde

Published in: Quantum Information Processing | Issue 7/2023

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Abstract

We formalize the notion of a sedentary vertex and present a relaxation of the concept of a sedentary family of graphs introduced by Godsil (Linear Algebra Appl 614:356–375, 2021. https://doi.org/10.1016/j.laa.2020.08.027). We provide sufficient conditions for a given vertex in a graph to exhibit sedentariness. We also show that a vertex with at least two twins (vertices that share the same neighbours) is sedentary. We prove that there are infinitely many graphs containing strongly cospectral vertices that are sedentary, which reveals that, even though strong cospectrality is a necessary condition for pretty good state transfer, there are strongly cospectral vertices which resist high probability state transfer to other vertices. Moreover, we derive results about sedentariness in products of graphs which allow us to construct new sedentary families, such as Cartesian powers of complete graphs and stars.

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Title: Sedentariness in quantum walks
Author: Hermie Monterde
Publication date: 01-07-2023
Publisher: Springer US
Published in: Quantum Information Processing / Issue 7/2023
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-023-04011-3

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