State Transfer In Graphs Research Articles

Quantifying state transfer strength on graphs with involution

This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the components of the eigenvectors of the Hamiltonian, it provides an approach to achieving high-fidelity state transfer by strategically selecting energy potentials based on the maximum degrees of the graphs. The study also involves an analysis of the time necessary for quantum transfer to occur.

Laplacian pair state transfer in vertex coronas

ABSTRACT Pair state transfer was introduced very recently, and there are only few results on the existence of pair state transfer in graphs. In this paper, we mainly study the existence of Laplacian pair state transfer in vertex coronas. We give sufficient conditions for vertex corona to have or to not have Laplacian perfect pair state transfer. We also give a sufficient condition for vertex corona to have Laplacian pretty good pair state transfer.

Perfect state transfer in NEPS of complete graphs

Perfect state transfer in graphs is a concept arising from quantum physics and quantum computing. Given a graph G with adjacency matrix AG, the transition matrix of G with respect to AG is defined as HAG(t)=exp(−itAG), t∈R,i=−1. We say that perfect state transfer from vertex u to vertex v occurs in G at time τ if u≠v and the modulus of the (u,v)-entry of HAG(τ) is equal to 1. If the moduli of all diagonal entries of HAG(τ) are equal to 1 for some τ, then G is called periodic with period τ. In this paper we give a few sufficient conditions for NEPS of complete graphs to be periodic or exhibit perfect state transfer.

State transfer and star complements in graphs

Let G be a graph with adjacency matrix A, and let H(t)=exp(itA). For an eigenvalue μ of A with multiplicity k, a star set for μ in G is a vertex set X of G such that |X|=k and the induced subgraph G−X does not have μ as an eigenvalue. G is said to have perfect state transfer from the vertex u to the vertex v if there is a time τ such that |H(τ)u,v|=1. The unitary operator H(t) has important applications in the transfer of quantum information. In this paper, we give an expression of H(t). For a star set X of graph G, perfect state transfer does not occur between any two vertices in X. We also give some results for the existence of perfect state transfer in a graph.