Related papers: Perfect transmission and parallel composition for …
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by…
Perfect (quantum) state transfer has been proved to be an effective model for quantum information processing. In this paper, we give a characterization of cubelike graphs having perfect edge state transfer. By using a lifting technique, we…
Coin and scattering are the two major formulations for discrete quantum walks models, each believed to have its own advantages in different applications. Although they are related in some cases, it was an open question their equivalence in…
Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…
The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
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 consider scattering and transport in interacting quantum wires that are connected to leads. Such a setup can be represented by a minimal model of interacting fermions with inhomogeneities in the form of sudden changes in interaction…
For a finite graph $G=(V,E)$ let $G^*$ be obtained by considering a random perfect matching of $V$ and adding the corresponding edges to $G$ with weight $\varepsilon$, while assigning weight 1 to the original edges of $G$. We consider…
Let $G$ be a graph with adjacency matrix $A$. The transition matrix of $G$ relative to $A$ is defined by $H_{A}(t):=\exp{(-itA)},\;t\in\Rl$. We say that the graph $G$ admits perfect state transfer between the verteices $u$ and $v$ at…
We propose an information-theoretic statistical model to describe the universal features of those chaotic scattering processes characterized by a prompt and an equilibrated component. The model, introduced in the past in nuclear physics,…
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum…
Let $X$ be a graph on $n$ vertices with with adjacency matrix $A$ and let $H(t)$ denote the matrix-valued function $\exp(iAt)$. If $u$ and $v$ are distinct vertices in $X$, we say perfect state transfer}from $u$ to $v$ occurs if there is a…
The quadratic unitary Cayley graph $\mathcal{G}_{\mathbb{Z}_n}$ has vertex set $\mathbb{Z}_n: =\{0,1, \ldots ,n-1\}$, where two vertices $u$ and $v$ are adjacent if and only if $u - v$ or $v-u$ is a square of some units in $\mathbb{Z}_n$.…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…
In this paper, we generalize the notions of perfect matchings, perfect 2-matchings to perfect k-matchings and give a necessary and sufficient condition for existence of perfect k-matchings. For bipartite graphs, we show that this k-matching…
This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…
We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of known structural results permitting to decompose perfect graphs into basic perfect graphs by means of two graph operations: 2-join and skew…