Multiparty entanglement in graph states

  title={Multiparty entanglement in graph states},
  author={Marc Hein and Jens Eisert and Hans J. Briegel},
  journal={Physical Review A},
Graph states are multiparticle 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 distributed quantum systems that play a significant role in quantum error correction, multiparty quantum communication, and quantum computation within the framework of the one-way quantum computer. We characterize and quantify the genuine multiparticle entanglement… 
Generalized graph states based on Hadamard matrices
This work proposes to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix, and studies the entanglement structures of these generalized graph states and shows that they are all maximally mixed locally.
Classification of the entanglement properties of eight-qubit graph states ∗
A n-qubit graph state |G〉 is a pure state associated to a graph G(V,E). The graph G provides both a recipe for preparing |G〉 and a mathematical characterization of |G〉 [4]. Graph states play several
A bonding model of entanglement for N-qubit graph states
The class of entangled N-qubit states known as graph states, and the corresponding stabilizer groups of N-qubit Pauli observables, have found a wide range of applications in quantum information
Transformations of Stabilizer States in Quantum Networks
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study
Quantum entanglement in non-local games, graph parameters and zero-error information theory
We study quantum entanglement and some of its applications in graph theory and zero-error information theory. In Chapter 1 we introduce entanglement and other fundamental concepts of quantum theory.
Experimental entanglement of six photons in graph states
Graph states1,2,3—multipartite entangled states that can be represented by mathematical graphs—are important resources for quantum computation4, quantum error correction3, studies of multiparticle
The Study of Entangled States in Quantum Computation and Quantum Information Science
It is proved that transversal gates are insufficient to achieve universal computation on almost all QECCs and constructed explicit quantum circuits that create entangling measurements are constructed, and show that these circuits scale polynomially in the input parameters.
Quantum entanglement in states generated by bilocal group algebras (9 pages)
Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an
Mapping graph state orbits under local complementation
This work finds direct links between the connectivity of certain orbits with the entanglement properties of their component graph states, and observes the correlations between graph-theoretical orbit properties, with Schmidt measure and preparation complexity and suggest potential applications.
Entanglement and local information access for graph states
It is shown that a number of multipartite entanglement measures evaluated give an operational interpretation as the maximal number of graph states distinguishable by local operations and classical communication (LOCC), as well as supplying a tight bound on the fixed letter classical capacity under LOCC decoding.


The Heisenberg Representation of Quantum Computers
Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features
Stabilizer Codes and Quantum Error Correction
An overview of the field of quantum error correction and the formalism of stabilizer codes is given and a number of known codes are discussed, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation are discussed.
Introduction to Graph Theory
1. Fundamental Concepts. What Is a Graph? Paths, Cycles, and Trails. Vertex Degrees and Counting. Directed Graphs. 2. Trees and Distance. Basic Properties. Spanning Trees and Enumeration.
Discrete math = 離散数学
What is discrete math? • The real numbers are continuous in the senses that: * between any two real numbers there is a real number • The integers do not share this property. In this sense the
Graph Theory
Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.
West,Introduction to Graph Theory(Prentice Hall
  • Upper Saddle River, NJ,
  • 2001
  • Rev. A 65, 012308
  • 2002
  • Rev. A 68, 022312
  • 2003
  • Rev. Lett. 86, 910
  • 2001
Quantum Computation and Information (Cambridge
  • 2000