München 2004 – scientific programme

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Q: Quantenoptik und Photonik

Q 2: Quanteninformation I

Q 2.4: Talk

Monday, March 22, 2004, 14:45–15:00, HS 101

Graph states — •J. Eisert¹, M. Hein², and H.-J. Briegel² — ¹Institut für Physik, Am Neuen Palais 10, Universität Potsdam, D-14469 Potsdam — ²Institut für theoretische Physik, Technikerstraße 25, Universität Innsbruck, A-6020 Innsbruck

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 distributed quantum systems that play a significant role in quantum error correction, multi-party quantum communication, and quantum computation within the framework of the one-way quantum computer. In this talk, the formalism and setting of graph states will be introduced. General transformation rules for graphs will be presented in graph theoretical language when local Pauli measurements are applied, and we will provide criteria for the equivalence of two graphs up to local unitary transformations. We also characterize and quantify the genuine multi-particle entanglement of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Examples will include the codewords of the concatenated [7,1,3]-CSS code and the graph states associated with the quantum Fourier transform in the one-way computer. (See also the subsequent talk by M. Hein, W. Dür, and H.J. Briegel.)