Related papers: Stateless Quantum Structures and Extremal Graph Th…
Graph states are a fundamental class of multipartite entangled quantum states with wide-ranging applications in quantum information and computation. In this work, we develop a systematic framework for constructing and analyzing…
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…
Provided a complete set of putative $k$-body reductions of a multipartite quantum state, can one determine if a joint state exists? We derive necessary conditions for this to be true. In contrast to what is known as the quantum marginal…
Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric…
An orthogonal representation of a graph is an assignment of nonzero real vectors to its vertices such that distinct non-adjacent vertices are assigned to orthogonal vectors. We prove general lower bounds on the dimension of orthogonal…
Graph states are an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes-quantum computers within which…
We determine the vertex-minor Ramsey number $\Rvm(4)=11$, where $\Rvm(k)$ is the smallest~$n$ such that every $n$-vertex graph contains the edgeless graph~$E_k$ as a vertex-minor. We prove this by an exhaustive classification of the graphs…
We provide several new results on quantum state space, on lattice of subspaces of an infinite dimensional Hilbert space, and on infinite dimensional Hilbert space equations as well as on connections between them. In particular we obtain an…
In this work, we construct and quantify asymptotically in the limit of large mass a variety of edge-localized stationary states of the focusing nonlinear Schr\"odinger equation on a quantum graph. The method is applicable to general bounded…
We design a series of quantum circuits that generate absolute maximally entangled (AME) states to benchmark a quantum computer. A relation between graph states and AME states can be exploited to optimize the structure of the circuits and…
We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in…
The hypercube Q_n is the graph whose vertex set is {0,1}^n and where two vertices are adjacent if they differ in exactly one coordinate. For any subgraph H of the cube, let ex(Q_n, H) be the maximum number of edges in a subgraph of Q_n…
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…
The study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have never been computed so far. We close this gap by proving that the quantum automorphism group of a finite, directed graph…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
Seeking a relativistic quantum infrastructure for gauge physics, we analyze spacetime into three levels of quantum aggregation analogous to atoms, bonds and crystals. Quantum spacetime points with no extension make up more complex link…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
We consider quantum graph states that can be mapped to directed weighted graphs, also known as directed networks. The geometric measure of entanglement of the states is calculated for the quantum graph states corresponding to arbitrary…
Graph states and their entanglement properties are pivotal for the development of quantum computing and technologies. For qubits, local complementation, a graphical rule that connects all the equivalent states under Local Clifford (LC)…
We consider the number \bar N(q) of points in the projective complement of graph hypersurfaces over \F_q and show that the smallest graphs with non-polynomial \bar N(q) have 14 edges. We give six examples which fall into two classes. One…