Related papers: Perfect state transfer in graphs related to linear…
Perfect state transfer (PST) has great significance due to its applications in quantum information processing and quantum computation. In this paper we present a characterization on connected simple Cayley graph $\Gamma={\rm Cay}(G,S)$…
We study pretty good quantum state transfer (i.e., state transfer that becomes arbitrarily close to perfect) between vertices of graphs with an involution in the presence of an energy potential. In particular, we show that if a graph has an…
This paper investigates perfect state transfer in Grover walks, a model of discrete-time quantum walks. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on graphs belonging to an association…
We introduce the concept of group state transfer on graphs, summarize its relationship to other concepts in the theory of quantum walks, set up a basic theory, and discuss examples. Let $X$ be a graph with adjacency matrix $A$ and consider…
We characterize perfect state transfer on real-weighted graphs of the Johnson scheme $\mathcal{J}(n,k)$. Given $\mathcal{J}(n,k)=\{A_1, A_2, \cdots, A_k\}$ and $A(X) = w_0A_0 + \cdots + w_m A_m$, we show, using classical number theory…
A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk…
Perfect state transfer between two marked vertices of a graph by means of discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit…
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,…
As generalizations of results of Christandl et al.\cite{8,9""} and Facer et al.\cite{Facer}, Bernasconi et al.\cite{godsil,godsil1} studied perfect state transfer (PST) between two particles in quantum networks modeled by a large class of…
In order to obtain perfect state transfer between two sites in a network of interacting qubits, their corresponding vertices in the underlying graph must satisfy a combinatorial property called strong cospectrality. Here we determine the…
Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state transfer in continuous-time quantum walks, which is…
A graph is said to exhibit perfect state transfer (PST) if one of its corresponding Hamiltonian matrices, which are based on the vertex-edge structure of the graph, gives rise to PST in a quantum information-theoretic context, namely with…
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…
We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.
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…
A continuous-time quantum walk on a graph evolves according to the unitary operator $e^{-iAt}$, where $A$ is the adjacency matrix of the graph. Perfect state transfer (PST) in a quantum walk is the transfer of a quantum state from one node…
We consider graphs with two cut vertices joined by a path with one or two edges, and prove that there can be no quantum perfect state transfer between these vertices, unless the graph has no other vertex. We achieve this result by applying…
In this paper, we study quantum walks on the extension of association schemes. Various state transfers can be achieved on these graphs, such as multiple state transfer among extreme points of a simplex, fractional revival on subsimplexes.…
A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in…
Let $G$ be a graph with adjacency matrix $A$. The transition matrix corresponding to $G$ is defined by $H(t):=\exp{\left(itA\right)}$, $t\in\Rl$. The graph $G$ is said to have perfect state transfer (PST) from a vertex $u$ to another vertex…