Related papers: Fractional revival on non-cospectral vertices
Quantum teleportation is rigorously discussed with coherent entang led states given by beam splittings. The mathematical scheme of beam splitti ng has been used to study quantum communication and quantum stochastic. We d iscuss the…
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
In this paper we study the protocol implementation and property analysis for several practical quantum secret sharing (QSS) schemes with continuous variable graph state (CVGS). For each QSS scheme, an implementation protocol is designed…
We study a transport phenomenon in certain coined quantum walks where a subspace of states localized at a vertex gets transferred to another vertex. We first develop characterizations for perfect and pretty good subspace state transfer…
We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any…
Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on the first observation of a perfect state transfer protocol on a…
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…
Multiple quantum (MQ) NMR coherence spectra, which can be obtained experimentally in MQ NMR, can be transferred from the sender to the remote receiver without mixing the MQ-coherences of different orders and distortions. The only effect of…
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 weighted graph $G$ with countable vertex set is bounded if there is an upper bound on the maximum of the sum of absolute values of all edge weights incident to a vertex in $G$. In this paper, we prove a fundamental result on equitable…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
Full state revivals in a quantum walk can be viewed as returning of the walker to the initial quantum state in a periodic fashion during the propagation of the walk. In this paper we show that for any given number of spatial dimensions, a…
Quantum spin networks can be used to transport information between separated registers in a quantum information processor. To find a practical implementation, the strict requirements of ideal models for perfect state transfer need to be…
Originating from spectral graph theory, cospectrality is a powerful generalization of exchange symmetry and can be applied to all real-valued symmetric matrices. Two vertices of an undirected graph with real edge weights are cospectral iff…
We present a generic treatment of wave-packet revivals for quantum-mechanical systems. This treatment permits a classification of certain ideal revival types. For example, wave packets for a particle in a one-dimensional box are shown to…
Weight-sharing is one of the pillars behind Convolutional Neural Networks and their successes. However, in physical neural systems such as the brain, weight-sharing is implausible. This discrepancy raises the fundamental question of whether…
We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We…
This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the eigenvectors of the Hamiltonian, it provides an approach to achieving high-fidelity state…
We introduce some new perfect state transfer and teleportation schemes by quantum walks with two coins. Encoding the transferred information in coin 1 state and alternatively using two coin operators, we can perfectly recover the…
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…