Related papers: Connectivity for quantum graphs
In recent years an increasing number of papers attempt to mimic or supplant quantum field theory in discussions of issues related to gravity by the tools and through the perspective of quantum information theory, often in the context of…
Quantum physics is known to allow for completely new ways to create, manipulate and store information. Quantum communication - the ability to transmit quantum information - is a primitive necessary for any quantum internet. At its core,…
A $k$-connected set in an infinite graph, where $k > 0$ is an integer, is a set of vertices such that any two of its subsets of the same size $\ell \leq k$ can be connected by $\ell$ disjoint paths in the whole graph. We characterise the…
An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…
Networks based on entangled quantum systems enable interesting applications in quantum information processing and the understanding of the resulting quantum correlations is essential for advancing the technology. We show that the theory of…
We present the construction of a new family of coherent states for quantum theories of connections obtained following the polymer quantization. The realization of these coherent states is based on the notion of graph change, in particular…
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
In the framework of Category Theory, we study the association between finite--dimensional representations of a compact quantum group and quantum vector bundles with linear connections for a given quantum principal bundle with a principal…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to…
The vertices of a $k$-token graph of a graph $G$ correspond to $k$ indistinguishable tokens placed on $k$ different vertices of $G$. Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex…
Large-scale communication networks, such as the internet, rely on routing packets of data through multiple intermediate nodes to transmit information from a sender to a receiver. In this paper, we develop a model of a quantum communication…
Quantum Bayesian networks provide a mathematical formalism to describe causal relations, to analyse correlations, and to predict the probabilities of measurement outcomes, in systems involving both classical and quantum data. They…
We prove that for every pair of quantum isomorphic graphs, their block trees and their block graphs are isomorphic, and that such an isomorphism can be chosen so that the corresponding blocks are quantum isomorphic -- in particular,…
Over the past several decades, the proliferation of global classical communication networks has transformed various facets of human society. Concurrently, quantum networking has emerged as a dynamic field of research, driven by its…
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between…
The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$ was introduced by Chartrand et al. in 1984, which is a nice generalization of the classical connectivity. Recently, as a natural counterpart, Li et al. proposed the concept of…
In this work we seek to generalize the connection between traversable wormholes and quantum channels. We do this via a connection between traversable wormholes and graph geometries on which we can perform quantum random walks for signal…
We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity.…