Pretty good state transfer on double stars

Hiranmoy Pal, Bikash Bhattacharjya

Joseph M. Renes

Sarojini Mohapatra, Hiranmoy Pal

A subdivided star SK1,l is obtained by identifying exactly one pendant vertex from l copies of the path P3. We consider the existence of quantum state transfer on double subdivided star Tl,m which is a pair of subdivided stars SK1,l and SK1,m joined by an edge to the respective coalescence vertices. We provide a complete characterization of double subdivided stars exhibiting pretty good state transfer. Although there is no perfect state transfer on double subdivided stars, we find perfect pair state transfer on Tl,m considering the adjacency matrix as the Hamiltonian of the corresponding quantum system.

Qiuting Chen, Chris D. Godsil

Sarojini Mohapatra, Hiranmoy Pal

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.

Hailong Hou, Rui Gu, Mengdi Tong

Abstract LetAbe the adjacency matrix of a graphGand supposeU(t) = exp(itA). We say that we have perfect state transfer inGfrom the vertexuto the vertexvat timetif there is a scalarγof unit modulus such thatU(t)eu=γ ev. It is known that perfect state transfer is rare. So C.Godsil gave a relaxation of this definition: we say that we have pretty good state transfer fromutovif there exists a complex numberγof unit modulus and, for each positive realϵthere is a timetsuch that ‖U(t)eu–γ ev‖ <ϵ. In this paper, the quantum state transfer on 1-sum of star graphsFk,lis explored. We show that there is no perfect state transfer onFk,l, but there is pretty good state transfer onFk,lif and only ifk=l.