Related papers: Perfect state transfer in cubelike graphs
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…
The $\mathcal{Q}$-graph of a graph $G$, denoted by $\mathcal{Q}(G)$, is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and adding a new edge between two new vertices which lie on adjacent edges of $G$. In this…
The transfer of a quantum state between distant nodes in two-dimensional networks, is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It…
Perfect state transfer and fractional revival can be used to move information between pairs of vertices in a quantum network. While perfect state transfer has received a lot of attention, fractional revival is newer and less studied. One…
Using graphs with clusters, we provide a unified approach for constructing graphs with pair state transfer-relative to the adjacency, Laplacian, and signless Laplacian matrix-between the same pair of states at the same time, despite being…
We propose a class of qubit networks that admit perfect transfer of any quantum state in a fixed period of time. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be…
The paper investigates perfect state transfer (PST) in Grover walks on Cayley graphs over the dihedral group $D_n$. The Grover walk is a discrete-time quantum walk widely studied in quantum information processing. A Cayley graph…
The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time…
We study perfect state transfer and multiple state transfer in oriented normal Cayley graphs. We construct examples in a variety of groups, ranging from abelian to nonsolvable, and establish some general restrictions and nonexistence…
We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks. In contrast, the infinite paths represent…
Let $R$ be a commutative ring with unity not equal to zero and let $\Gamma(R)$ be a zero-divisor graph realized by $R$. For a simple, undirected, connected graph $G = (V, E)$, a {\it total perfect code} denoted by $C(G)$ in $G$ is a subset…
In a continuous-time quantum walk on a network of qubits, pretty good state transfer is the phenomenon of state transfer between two vertices with fidelity arbitrarily close to 1. We construct families of graphs to demonstrate that there is…
In this paper, we consider the problem on the existence of perfect state transfer(PST for short) on semi-Cayley graphs over abelian groups (which are not necessarily regular), i.e on the graphs having semiregular and abelian subgroups of…
We introduce a scheme for perfect state transfer in regular two and three dimensional structures. The interactions on the lattices are of XX spin type with uniform couplings. In two dimensions the structure is a hexagonal lattice and in…
We completely characterize circulant graphs with valency up to $4$ that admit perfect state transfer. Those of valency $3$ do not admit it. On the other hand, circulant graphs with valency $4$ admit perfect state transfer only in two…
Given a graph $\Gamma$, a perfect code in $\Gamma$ is an independent set $C$ of vertices of $\Gamma$ such that every vertex outside of $C$ is adjacent to a unique vertex in $C$, and a total perfect code in $\Gamma$ is a set $C$ of vertices…
A recent numerical study of short chains found near-perfect quantum state transfer between the boundary sites of a spin-1/2 XX chain if a sufficiently strong magnetic field acts on these sites. We show that the phenomenon is based on a pair…
We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties,…
We introduce and study peak state transfer, a notion of high state transfer in qubit networks modeled by continuous-time quantum walks. Unlike perfect or pretty good state transfer, peak state transfer does not require fidelity arbitrarily…
By considering distance-regular graphs as spin networks, first we introduce some particular spin Hamiltonians which are extended version of those of Refs.\cite{8,9''}. Then, by using spectral analysis techniques and algebraic combinatoric…