Related papers: Laplacian pair state transfer in Q-graph
We study how far a diffusion process on a graph can deviate from a designed starting pattern when the pattern is generated via Laplacian regularisation. Under standard stability conditions for undirected, entrywise nonnegative graphs, we…
The power graph \( \mathcal{G}_G \) of a group \( G \) is a graph whose vertex set is \( G \), and two elements \( x, y \in G \) are adjacent if one is an integral power of the other. In this paper, we determine the adjacency, Laplacian,…
A vertex in a graph is said to be sedentary if a quantum state assigned on that vertex tends to stay on that vertex. Under mild conditions, we show that the direct product and join operations preserve vertex sedentariness. We also…
Cubelike graphs are the Cayley graphs of the elementary abelian group (Z_2)^n (e.g., the hypercube is a cubelike graph). We give conditions for perfect state transfer between two particles in quantum networks modeled by a large class of…
We give a complete characterization of pretty good state transfer on paths between any pair of vertices with respect to the quantum walk model determined by the XY-Hamiltonian. If $n$ is the length of the path, and the vertices are indexed…
On a finite regular graph, (co)resonant states are eigendistributions of the transfer operator associated to the shift on one-sided infinite non-backtracking paths. We introduce two pairings of resonant and coresonant states, the vertex…
The neighborhood corona $G \star H$ is the graph obtained by taking one copy $G$ and $|G|$ copies of $H$, and joining each vertex of the $j$th copy of $H$ to all neighbors of $v_{j}$ in $G$. In this paper, we study the state transfer of…
We investigate quantum and nonsignaling generalizations of perfect matchings in graphs using nonlocal games. Specifically, we introduce nonlocal games that test for $L$-perfect matchings in bipartite graphs, perfect matchings in general…
A general formalism of the problem of perfect state transfer is presented. We show that there are infinitely many Hamiltonians which may provide solution to this problem. In a first attempt to give a classification of them we investigate…
We propose a protocol for perfect state transfer between any pair of vertices in a hypercube. Given a pair of distinct vertices in the hypercube we determine a sub-hypercube that contains the pair of vertices as antipodal vertices. Then a…
We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by…
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…
Quantum state transfer in a triangular domain of a two-dimensional, equally-spaced, spin lat- tice with non-homogeneous nearest-neighbor couplings is analyzed. An exact solution of the one- excitation dynamics is provided in terms of…
We consider an exact state transmission, where a density matrix in one information processor A at time $t=0$ is exactly equal to that in another processor B at a later time. We demonstrate that there always exists a complete set of…
Graph states are an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes-quantum computers within which…
Graph states are key resources for measurement-based quantum computing, which is particularly promising for photonic systems. Fusions are probabilistic Bell state measurements, measuring pairs of parity operators of two qubits. Fusions can…
We study transfer of single photon in an one-dimensional finite Glauber-Fock cavity array whose coupling strengths satisfy a square root law. The evolved state in the array can be mapped to an upper truncated coherent state if the cavities…
We consider a generalization of the diffusion equation on graphs. This generalized diffusion equation gives rise to both normal and superdiffusive processes on infinite one-dimensional graphs. The generalization is based on the $k$-path…
Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying…
We investigate quantum state transfer on a class of bipartite graphs, namely the butterfly graphs, within the framework of discrete-time quantum walks. These graphs facilitate the construction of scalable quantum networks that enable…