Related papers: Vector Representations of Graphs and Distinguishin…
We bring together in one place some of the main results and applications from our recent works in quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time…
We investigate a graph-theoretic approach to the problem of distinguishing quantum product states in the fundamental quantum communication framework called local operations and classical communication (LOCC). We identify chordality as the…
The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a…
Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
Graph states are a class of multi-partite entangled quantum states that are ubiquitous in quantum information. We study equivalence relations between graph states under local unitaries (LU) to obtain distinguishing methods both in local and…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…
In this paper, we propose a new way to represent graphs in quantum space. In that approach, we replace the rows of the adjacency matrix of the graph by state vectors in the occupation number representation. Unlike the traditional definition…
Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…
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 consider deeply the relation between the orthogonality and the distinguishability of a set of arbitrary states (including multi-partite states). It is shown that if a set of arbitrary states can be distinguished by local operations and…
The name graph state is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
We explore the intersection of studies in quantum error correction and quantum local operations and classical communication (LOCC). We consider one-way LOCC measurement protocols as quantum channels and investigate their error correction…
In the first part of this Dissertation, I study the differences between LOCC (local operations and classical communication) and the more general class of separable operations. I show that the two classes coincide for the case of pure…
This workshop brought together experts in classical graph theory and quantum information science to explore the intersection of these fields, with a focus on quantum graph states and their applications in computing, networking, and sensing.…
We develop graph theoretic methods for analysing maximally entangled pure states distributed between a number of different parties. We introduce a technique called {\it bicolored merging}, based on the monotonicity feature of entanglement…
Lattice states are a class of quantum states that naturally generalize the fundamental set of Bell states. We apply recent results from quantum error correction and from one-way local operations and classical communication (LOCC) theory,…