arXiv:2603.17595

Pretty good plus state transfer in cycles

Sarojini Mohapatra, Hiranmoy Pal

math.COquant-phSubmitted Mar 18, 2026• Announced Mar 19, 2026

Abstract

We investigate fractional revival in graphs with respect to the adjacency, Laplacian, and signless Laplacian matrices. We observe that, under certain conditions, fractional revival is preserved under graph complementation. Then we establish a connection between fractional revival in a graph and in its double cover, and obtain a complete characterization of pretty good plus state transfer in cycles and their complements. This leads to characterizations of pretty good vertex state transfer in weighted paths with potential.

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arXiv:2603.17595

Pretty good plus state transfer in cycles

Sarojini Mohapatra, Hiranmoy Pal

math.COquant-phSubmitted Mar 18, 2026• Announced Mar 19, 2026

arXiv HTML PDF

Abstract

Related papers

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The complementary prism

G\overline{G}

of a graph

G

is obtained from the disjoint union of

G

and its complement

\overline{G}

by adding an edge between each vertex

a

G

and its copy

a'

\overline{G}.

This paper explores a general framework for studying fractional revival with respect to real symmetric matrices with a block structure. The framework is then used to show that, for a fixed state

\mathbf{u}

G

orthogonal to the all-one vector, the complementary prism

G\overline{G}

exhibits fractional revival from the state

[\mathbf{u},\mathbf{0}]^T

with respect to the adjacency, Laplacian, and signless Laplacian matrices. We further characterize perfect pair state transfer in the complementary prism of a complete graph and establish the existence of perfect pair and plus state transfer in the complementary prism of a complete bipartite graph.

Given a graph

G

with vertex set

V(G)=\{v_1,v_2,\ldots,v_{n_1}\}

and a graph

H

of order

n_2

, the vertex complemented corona, denoted by

G\tilde{\circ}{H}

, is the graph produced by copying

H

n_1

times, with the

i

-th copy of

H

corresponding to the vertex

v_i

, and then adding edges between any vertex in

V(G)\setminus\{v_{i}\}

and any vertex of the

i

-th copy of

H

. The present article deals with quantum state transfer of vertex complemented coronae concerning signless Laplacian matrix. Our research investigates conditions in which signless Laplacian perfect state transfer exists or not on vertex complemented coronae. Additionally, we also provide some mild conditions for the class of graphs under consideration that allow signless Laplacian pretty good state transfer.