Abstract
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 of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Several examples and classes of graphs will be discussed, where these bounds coincide. These examples include trees, cluster states of different dimensions, graphs that occur in quantum error correction, such as the concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier transform in the one-way computer. We also present general transformation rules for graphs when local Pauli measurements are applied, and give criteria for the equivalence of two graphs up to local unitary transformations, employing the stabilizer formalism. For graphs of up to seven vertices we provide complete characterization modulo local unitary transformations and graph isomorphisms.
Hein, M;
[1]
Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)];
Eisert, J;
[2]
Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)];
Briegel, H J;
[1]
Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria);
Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)]
- Theoretische Physik, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, D-80333 Munich (Germany)
- Institut fuer Physik, Universitaet Potsdam, Am Neuen Palais 10, D-14469 Potsdam (Germany)
Citation Formats
Hein, M, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)], Eisert, J, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)], Briegel, H J, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria), and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)].
Multiparty entanglement in graph states.
United States: N. p.,
2004.
Web.
doi:10.1103/PhysRevA.69.062311.
Hein, M, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)], Eisert, J, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)], Briegel, H J, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria), & Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)].
Multiparty entanglement in graph states.
United States.
https://doi.org/10.1103/PhysRevA.69.062311
Hein, M, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)], Eisert, J, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)], Briegel, H J, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria), and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)].
2004.
"Multiparty entanglement in graph states."
United States.
https://doi.org/10.1103/PhysRevA.69.062311.
@misc{etde_20643736,
title = {Multiparty entanglement in graph states}
author = {Hein, M, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)], Eisert, J, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)], Briegel, H J, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria), and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)]}
abstractNote = {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 of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Several examples and classes of graphs will be discussed, where these bounds coincide. These examples include trees, cluster states of different dimensions, graphs that occur in quantum error correction, such as the concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier transform in the one-way computer. We also present general transformation rules for graphs when local Pauli measurements are applied, and give criteria for the equivalence of two graphs up to local unitary transformations, employing the stabilizer formalism. For graphs of up to seven vertices we provide complete characterization modulo local unitary transformations and graph isomorphisms.}
doi = {10.1103/PhysRevA.69.062311}
journal = []
issue = {6}
volume = {69}
place = {United States}
year = {2004}
month = {Jun}
}
title = {Multiparty entanglement in graph states}
author = {Hein, M, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)], Eisert, J, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)], Briegel, H J, Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria), and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)]}
abstractNote = {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 of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Several examples and classes of graphs will be discussed, where these bounds coincide. These examples include trees, cluster states of different dimensions, graphs that occur in quantum error correction, such as the concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier transform in the one-way computer. We also present general transformation rules for graphs when local Pauli measurements are applied, and give criteria for the equivalence of two graphs up to local unitary transformations, employing the stabilizer formalism. For graphs of up to seven vertices we provide complete characterization modulo local unitary transformations and graph isomorphisms.}
doi = {10.1103/PhysRevA.69.062311}
journal = []
issue = {6}
volume = {69}
place = {United States}
year = {2004}
month = {Jun}
}