Related papers: Quantum association schemes
Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here,…
We derive a formula for the level spacing probability distribution in quantum graphs. We apply it to simple examples and we discuss its relation with previous work and its possible application in more general cases. Moreover, we derive an…
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
We consider the representation of a continuous-time quantum walk in a graph $X$ by the matrix $\exp(itA(X))$. We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to…
Quantum graphs have been introduced by Duan, Severini, and Winter to describe the zero-error behaviour of quantum channels. Since then, quantum graph theory has become a field of study in its own right. A substantial source of difficulty in…
For a set of quantum states generated by the action of a group, we consider the graph obtained by considering two group elements adjacent whenever the corresponding states are non-orthogonal. We analyze the structure of the connected…
We give a definition of associative schemes, schemes of associative rings, over a field $k,$ using the definition of completion of an associative $k$-algebra in a finite set of simple modules. We start by giving a weaker but sufficient…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…
Strong cospectrality is an equivalence relation on the set of vertices of a graph that is of importance in the study of quantum state transfer in graphs. We construct families of abelian Cayley graphs in which the number of mutually…
An association scheme is $P$-polynomial if and only if it consists of the distance matrices of a distance-regular graph. Recently, bivariate $P$-polynomial association schemes of type $(\alpha,\beta)$ were introduced by Bernard et al., and…
A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which…
Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
We provide a definition of the quantum distances of correlated many fermion wave functions in terms of the expectation values of certain operators that we call exchange operators. We prove that the distances satisfy the triangle…
We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any…
We present an integral formalism for constructing scheme transformations in a quantum field theory. We apply this to generate several new useful scheme transformations. A comparative analysis is given of these scheme transformations in…
Recently, the work on quantum automorphism groups of graphs has seen renewed progress, which we expand in this paper. Quantum symmetry is a richer notion of symmetry than the classical symmetries of a graph. In general, it is non-trivial to…
We review recent progress in understanding the physical meaning of quantum graph models through analysis of their vertex coupling approximations.