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The graph state formalism is a useful abstraction of entanglement. It is used in some multipartite purification schemes and it adequately represents universal resources for measurement-only quantum computation. We focus in this paper on the…

Quantum Physics · Physics 2007-05-23 Mehdi Mhalla , Simon Perdrix

Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well--established notion of graph states. Mathematically, they can conveniently be described by a…

Quantum Physics · Physics 2014-08-11 O. Gühne , M. Cuquet , F. E. S. Steinhoff , T. Moroder , M. Rossi , D. Bruß , B. Kraus , C. Macchiavello

This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian. We show that the presence or absence of edges in the graph plays a pivotal role in defining the…

Quantum Physics · Physics 2024-01-05 Anoopa Joshi , Parvinder Singh , Atul Kumar

A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…

Data Structures and Algorithms · Computer Science 2010-09-07 Marko A. Rodriguez , Peter Neubauer

The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical…

Quantum Physics · Physics 2015-06-26 Bei Zeng , Hyeyoun Chung , Andrew W. Cross , Isaac L. Chuang

Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum…

Quantum Physics · Physics 2014-04-23 B. A. Bell , D. A. Herrera-Martí , M. S. Tame , D. Markham , W. J. Wadsworth , J. G. Rarity

The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…

Quantum Physics · Physics 2007-05-23 Dirk Schlingemann

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…

Quantum Physics · Physics 2024-10-01 Kh. P. Gnatenko

Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation…

Quantum Physics · Physics 2015-02-06 David W. Lyons , Daniel J. Upchurch , Scott N. Walck , Chase D. Yetter

Quantum hypergraph states extend the well-studied class of graph states by taking into account multi-qubit interactions through hyperedges. They provide a powerful framework to represent a family of quantum states with genuine multipartite…

Quantum Physics · Physics 2026-03-12 Davide Poderini , Dagmar Bruß , Chiara Macchiavello

The entanglement of graph states up to eight qubits is calculated in the regime of iteration calculation. The entanglement measures could be the relative entropy of entanglement, the logarithmic robustness or the geometric measure. All 146…

Quantum Physics · Physics 2015-05-14 Xiao-yu Chen

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…

Quantum Physics · Physics 2018-05-16 Axel Dahlberg , Stephanie Wehner

The form of a local Clifford (LC, also called local Gaussian (LG)) operation for the continuous-variable (CV) weighted graph states is presented in this paper, which is the counterpart of the LC operation of local complementation for qubit…

Quantum Physics · Physics 2009-11-13 Jing Zhang

We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…

Quantum Physics · Physics 2026-04-29 Harikrishnan K J , Amit Kumar Pal

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…

Quantum Physics · Physics 2007-05-23 M. Hein , J. Eisert , H. J. Briegel

Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of…

Quantum Physics · Physics 2020-08-18 David Amaro , Markus Müller , Amit Kumar Pal

We propose schemes to extract arbitrary graph states from two-dimensional cluster states by locally manipulating the qubits solely via single-qubit measurements. We introduce graph state manipulation tools that allow one to increase the…

Quantum Physics · Physics 2025-10-13 Julia Freund , Alexander Pirker , Lina Vandré , Wolfgang Dür

Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a…

Discrete Mathematics · Computer Science 2016-08-25 Karthekeyan Chandrasekaran , Corinna Gottschalk , Jochen Könemann , Britta Peis , Daniel Schmand , Andreas Wierz

Many experiments in quantum information aim at creating graph states. Quantifying the purity of an experimentally achieved graph state could in principle be accomplished using full-state tomography. This method requires a number of…

Quantum Physics · Physics 2010-10-12 Harald Wunderlich , Martin B. Plenio

The hypergraph states are pure multipartite quantum states corresponding to a hypergraph. It is an equal superposition of the states belonging to the computational basis. Given any hypergraph, we can construct a hypergraph state determined…

Combinatorics · Mathematics 2022-12-22 Supriyo Dutta