相关论文: Laplacian State Transfer in Coronas

Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…

In the quest for designing novel protocols for quantum information and quantum computation, an important goal is to achieve perfect quantum state transfer for systems beyond the well-known one dimensional cases, such as 1d spin chains. We…

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…

We prove Haag duality property of any translation invariant pure state on $\clb = \otimes_{\IZ}M_d(C), \;d \ge 2$, where $M_d(C)$ is the set of $d \times d$ dimensional matrices over field of complex numbers. We also prove a necessary and…

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 settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein {\it et al.} [Phys. Rev. A \textbf{73}, 012320 (2006)]. The conjecture states…

Theory predicts that double layer systems realize "two-component composite fermions," which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid and crystal…

Based on the Lyapunov control, we present a scheme to realize state transfer with high fidelity by only modulating the boundary spins in a quantum spin-1/2 chain. Recall that the conventional transmission protocols aim at nonstationary…

Given two signed graphs $\Gamma_1$ with nodes $\{u_1,u_2,\cdots,u_n\}$ and $\Gamma_2$, the neighbourhood corona, $\Gamma_1*\Gamma_2$ is the signed graph obtained by taking one copy of $\Gamma_1$ and $n_1$ copies of $\Gamma_2$, and joining…

We present several protocols for reliable quantum state transfer through a spin chain. We use a simple two-spin encoding to achieve a remarkably high fidelity transfer for an arbitrary quantum state. The fidelity of the transfer also…

Ho proved in [A note on the total domination number, Util.Math. 77 (2008) 97--100] that the total domination number of the Cartesian product of any two graphs with no isolated vertices is at least one half of the product of their total…

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…

The hardcore model is a model of lattice gas systems which has received much attention in statistical physics, probability theory and theoretical computer science. It is the probability distribution over independent sets $I$ of a graph…

In a recent work Grappin et al. [1] have shown that low- frequency movements can be transmitted from one footpoint to the other along a magnetic loop, thus mimicking a friction effect of the corona on the photosphere, and invalidating the…

In this work we consider the Laplacian controllability of a graph constructed by interconnecting a finite number of single-input Laplacian controllable graphs. We first study the interconnection realized by the composite graph of two…

A path in an edge-colored graph is called proper if no two consecutive edges of the path receive the same color. For a connected graph $G$, the proper connection number $pc(G)$ of $G$ is defined as the minimum number of colors needed to…

In a previous paper, we defined a version of the percolation triangle condition that is suitable for the analysis of bond percolation on a finite connected transitive graph, and showed that this triangle condition implies that the…

Graph burning is a discrete time process which can be used to model the spread of social contagion. One is initially given a graph of unburned vertices. At each round (time step), one vertex is burned; unburned vertices with at least one…

In this paper we explore some results concerning the spread of the line and the total graph of a given graph. In particular, it is proved that for an $(n,m)$ connected graph $G$ with $m > n \geq 4$ the spread of $G$ is less than or equal to…

We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic way. We obtain a deterministic limit shape in the scaling…