Related papers: Connectivity for quantum graphs
Mixed connectivity is a generalization of vertex and edge connectivity. A graph is $(p,0)$-connected, $p>0$, if the graph remains connected after removal of any $p-1$ vertices. A graph is $(p,q)$-connected, $p\geq 0$, $q>0$, if it remains…
Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication…
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…
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…
It is well known that quantum theory forbids the exact copying of an unknown quantum state. Therefore in broadcasting of classical information by a quantum channel an additional contribution to the error in the decoding is expected. We…
Quantum networks rely on both quantum and classical channels for coordinated operation. Current architectures employ entanglement distribution and key exchange over quantum channels but often assume that classical communication is…
We formulate the notion of quantum channels in the framework of quantum tomography and address there the issue of whether such maps can be regarded as classical stochastic maps. In particular kernels of maps acting on probability…
We introduce a new concept of Quantum Wrapper Networking, which enables control, management, and operation of quantum networks that can co-exist with classical networks while keeping the requirements for quantum networks intact. The quantum…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…
Classical communication is the basis for many of our current and future technologies, such as mobile phones, video conferences, autonomous vehicles and particularly the internet. In contrast, quantum communication is governed by the laws of…
This work re-examines a classical construction of a 2-connected (simple) graph where every intermediate graph is 2-connected before detailing an analogous construction for 3-connected graphs which requires a graph equivalence relation…
Expander graphs are fundamental in both computer science and mathematics, with a wide array of applications. With quantum technology reshaping our world, quantum expanders have emerged, finding numerous uses in quantum information theory,…
The "noncommutative graphs" which arise in quantum error correction are a special case of the quantum relations introduced in [N. Weaver, Quantum relations, Mem. Amer. Math. Soc. 215 (2012), v-vi, 81-140]. We use this perspective to…
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…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
Entanglement is a key resource in quantum communication, but bipartite schemes are often insufficient for advanced protocols like quantum secret sharing or distributed computing. Graph states offer a flexible way to represent and manage…