Related papers: Quantum state transfer between twins in weighted graphs

Quantum state transfer between twins in weighted graphs

URL: http://arxiv.org/abs/2201.02720v3
Date: Thu, 12 Jan 2023 20:02:57 GMT
Title: Quantum state transfer between twins in weighted graphs
Authors: Stephen Kirkland, Hermie Monterde and Sarah Plosker
Abstract summary: We explore the role of twin vertices in quantum state transfer. We provide characterizations of periodicity, perfect state transfer, and pretty good state transfer. As an application, we provide characterizations of all simple unweighted double cones on regular graphs that exhibit periodicity, perfect state transfer, and pretty good state transfer.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Twin vertices in simple unweighted graphs are vertices that have the same neighbours and, in the case of weighted graphs with possible loops, the corresponding incident edges have equal weights. In this paper, we explore the role of twin vertices in quantum state transfer. In particular, we provide characterizations of periodicity, perfect state transfer, and pretty good state transfer between twin vertices in a weighted graph with respect to its adjacency, Laplacian and signless Laplacian matrices. As an application, we provide characterizations of all simple unweighted double cones on regular graphs that exhibit periodicity, perfect state transfer, and pretty good state transfer.

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