Related papers: The Perfect State Transfer Graph Limbo
A continuous-time quantum walk on a graph is a matrix-valued function $\exp(-\mathtt{i} At)$ over the reals, where $A$ is the adjacency matrix of the graph. Such a quantum walk has universal perfect state transfer if for all vertices $u,v$,…
As quantum information technologies advance, challenges in scaling and connectivity persist, particularly the need for long-range qubit connectivity and efficient entanglement generation. Perfect State Transfer enables time-optimal state…
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 examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out. We also provide new examples…
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…
In this paper, we investigate a high-dimensional quantum state transfer protocol. An arbitrary unknown high-dimensional state can be transferred with high fidelity between two remote registers through a XX coupling spin chain of arbitrary…
The transport of quantum states is a crucial aspect of information processing systems, facilitating operations such as quantum key distribution and inter-component communication within quantum computers. Most quantum networks rely on…
Search and state transfer between hubs, i.e. fully connected vertices, on otherwise arbitrary connected graph is investigated. Motivated by a recent result of Razzoli et al. (J. Phys. A: Math. Theor. 55, 265303 (2022)) on universality of…
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…
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…
An $s$-pair state in a graph is a quantum state of the form $\mathbf{e}_u+s\mathbf{e}_v$, where $u$ and $v$ are vertices in the graph and $s$ is a non-zero complex number. If $s=-1$ (resp., $s=1$), then such a state is called a pair state…
High-fidelity quantum state transfer is critical for quantum communication and scalable quantum computation. Current quantum state transfer algorithms on the complete bipartite graph, which are based on discrete-time quantum walk search…
Effective routing of entanglements over a quantum network is a fundamental problem in quantum communication. Due to the fragility of quantum states, it is difficult to route entanglements at long distances. Graph states can be utilized for…
We show that using a slightly modified XX model for a spin-1/2 chain, one can transmit almost perfectly a maximally entangled two-qubit state from one end of the chain to the other one. This is accomplished without external fields or…
We investigate coined quantum walk search and state transfer algorithms, focusing on the complete $M$-partite graph with $N$ vertices in each partition. First, it is shown that by adding a loop to each vertex the search algorithm finds the…
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…
We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-1/2 network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and…
We describe new constructions of graphs which exhibit perfect state transfer on continuous-time quantum walks. Our constructions are based on variants of the double cones [BCMS09,ANOPRT10,ANOPRT09] and the Cartesian graph products (which…
Effective state transfer is one of the most important problems in quantum information processing. Typically, a quantum information device is composed of many subsystems with multi-input ports. In this paper, we develop a general theory…
We consider quantum state transfer relative to the Laplacian matrix of a graph. Let $N(u)$ denote the set of all neighbors of a vertex $u$ in a graph $G$. A pair of vertices $u$ and $v$ are called twin vertices of $G$ provided…