Related papers: Pretty Good State Transfer and Minimal Polynomials
The XX model with uniform couplings represents the most natural choice for quantum state transfer through spin chains. Given that it has long been established that single-qubit states cannot be transferred with perfect fidelity in this…
In this paper, we first give a necessary and sufficient condition for a graph to have Laplacian pretty good pair state transfer. As an application of such result, we give a complete characterization of Laplacian pretty good edge state…
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 quantify the effect of weighted loops at the source and target nodes of a graph on the strength of quantum state transfer between these vertices. We give lower bounds on loop weights that guarantee strong transfer fidelity that works for…
Perfect quantum state transfer is achievable in different settings, including linear qubit chains, bi-dimensional arrays, ladders, etc. The most studied case contemplates transferring arbitrary one-qubit pure states in systems with…
A simple method for transmitting quantum states within a quantum computer is via a quantum spin chain---that is, a path on $n$ vertices. Unweighted paths are of limited use, and so a natural generalization is to consider weighted paths;…
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…
We study perfect state transfer in Grover walks, which are typical discrete-time quantum walk models. In particular, we focus on states associated to vertices of a graph. We call such states vertex type states. Perfect state transfer…
We consider a quantum walk with two marked vertices, sender and receiver, and analyze its application to perfect state transfer on complete bipartite graphs. First, the situation with both the sender and the receiver vertex in the same part…
We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph $G$ has perfect state transfer if and only if its quotient $G/\pi$, under any equitable partition $\pi$, has perfect state transfer, we…
Perfect state transfer is significant in quantum communication networks. There are very few graphs having this property. So, it is useful to find some new graphs having perfect state transfer. A good way to construct new graphs is by…
A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in…
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…
In this paper we study quantum state transfer (also called quantum tunneling) on graphs when there is a potential function on the vertex set. We present two main results. First, we show that for paths of length greater than three, there is…
We explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. We extend the notion of adjacency strong cospectrality to arbitrary Hermitian matrices, with focus on the…
Previously it was shown that (almost) perfect state transfer can be achieved on the complete bipartite graph by a discrete-time coined quantum walk based algorithm when both the sender and receiver vertices are in the same partition 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 study perfect state transfer in Grover walks on two important classes of graphs: strongly regular graphs and strongly walk-regular graphs. The latter class is a generalization of the former. We first give a complete classification of…
We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks. In contrast, the infinite paths represent…
The question of perfect state transfer existence in quantum spin networks based on weighted graphs has been recently presented by many authors. We give a simple condition for characterizing weighted circulant graphs allowing perfect state…