A Characterization of Global Entanglement |
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| Authors: | Peter J. Love Alec Maassen van den Brink A. Yu. Smirnov M. H. S. Amin M. Grajcar E. Il’ichev A. Izmalkov A. M. Zagoskin |
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| Affiliation: | (1) Department of Physics, Haverford College, 370, Lancaster Avenue, Haverford, PA 19041-1392, USA;(2) D-Wave Systems Inc., 100-4401 Still Creek Drive, Burnaby, B.C., Canada, V5C 6G9;(3) Department of Mathematics, Tufts University, Bromfield–Pearson Building, Medford, MA 02155, USA;(4) Frontier Research System, RIKEN, Wako-shi, Saitama 351-0198, Japan;(5) Institute for Physical High Technology, P.O. Box 100239, D-07702 Jena, Germany;(6) Department of Solid State Physics, Comenius University, SK-84248 Bratislava, Slovakia;(7) Physics and Astronomy Dept., The University of British Columbia, 6224 Agricultural Rd., Vancouver, B.C., Canada, V6T 1Z1 |
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| Abstract: | We define a set of 2 n−1−1 entanglement monotones for n qubits and give a single measure of entanglement in terms of these. This measure is zero except on globally entangled (fully inseparable) states. This measure is compared to the Meyer–Wallach measure for two, three, and four qubits. We determine the four-qubit state, symmetric under exchange of qubit labels, which maximizes this measure. It is also shown how the elementary monotones may be computed as a function of observable quantities. We compute the magnitude of our measure for the ground state of the four-qubit superconducting experimental system investigated in [M. Grajcar et al., Phys. Rev. Lett. 96, 047006 (2006)], and thus confirm the presence of global entanglement in the ground state. |
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| Keywords: | Meyer– Wallach measure elementary monotones entanglement monotones global entanglement four-qubit state qubit labels |
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