Related papers: Quantum Fractional Revival on Graphs
Fractional revival, known as a quantum transport phenomenon, is essential for entanglement generation in quantum spin networks. The concept of fractional revival is a generalization of perfect state transfer and periodicity on graphs. In…
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is…
We initiate the study of approximate quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of approximate fractional revival in a graph in terms of the…
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…
We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and strongly cospectral vertices to arbitrary subsets of…
A systematic study of fractional revival at two sites in $XX$ quantum spin chains is presented and analytic models with this phenomenon are exhibited. The generic models have two essential parameters and a revival time that does not depend…
In this article, we give characterization for existence of quantum fractional revival in unitary Cayley graph utilizing adjacency matrix Hamiltonian. Unitary Cayley graph $X=( Z_n, S)$ is a special graph as connection set $S \subseteq Z_n$…
The occurrence of fractional revival in quantum spin chains is examined. Analytic models where this phenomenon can be exhibited in exact solutions are provided. It is explained that spin chains with fractional revival can be obtained by…
An example of a graph that admits balanced fractional revival between antipodes is presented. It is obtained by establishing the correspondence between the quantum walk on a hypercube where the opposite vertices across the diagonals of each…
We develop the theory of fractional revival in the quantum walk on a graph using its Laplacian matrix as the Hamiltonian. We first give a spectral characterization of Laplacian fractional revival, which leads to a polynomial time algorithm…
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…
Fractals are fascinating structures, not only for their aesthetic appeal, but also because they allow for the investigation of physical properties in non-integer dimensions. In these unconventional systems, a myriad of intrinsic features…
We develop the theory of pretty good quantum fractional revival in arbitrary sized subsets of a graph, including the theory for fractional cospectrality of subsets of arbitrary size. We use this theory to give conditions under which a…
The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites.…
Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially…
In this paper, we provide a characterization of fractional revival between twin vertices in a weighted graph with respect to its adjacency, Laplacian and signless Laplacian matrices. As an application, we characterize fractional revival…
Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier…
This paper extends the theory of quantum fractional revival (QFR) on unitary Cayley graphs $X=(V(\mathbb{Z}_n),E(S))$ in several directions that remained unresolved in previous work. First, we investigate QFR with respect to the Laplacian…
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution,…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…