A Characterization of Global Entanglement

  • Authors:

  • Peter J. Love;Alec Maassen Brink;A. Yu. Smirnov;M. H. Amin;M. Grajcar;E. Il'Ichev;A. Izmalkov;A. M. Zagoskin

  • Affiliations:

  • Department of Physics, Haverford College, Haverford, USA 19041-1392 and D-Wave Systems Inc., Burnaby, Canada V5C 6G9 and Department of Mathematics, Tufts University, Medford, USA 02155;D-Wave Systems Inc., Burnaby, Canada V5C 6G9 and Frontier Research System, RIKEN, Wako-shi, Saitama, Japan 351-0198;D-Wave Systems Inc., Burnaby, Canada V5C 6G9 and Frontier Research System, RIKEN, Wako-shi, Saitama, Japan 351-0198;D-Wave Systems Inc., Burnaby, Canada V5C 6G9;Frontier Research System, RIKEN, Wako-shi, Saitama, Japan 351-0198 and Institute for Physical High Technology, Jena, Germany D-07702 and Department of Solid State Physics, Comenius University, Bra ...;Institute for Physical High Technology, Jena, Germany D-07702;Institute for Physical High Technology, Jena, Germany D-07702;Frontier Research System, RIKEN, Wako-shi, Saitama, Japan 351-0198 and Physics and Astronomy Dept., The University of British Columbia, Vancouver, Canada V6T 1Z1

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2007

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Abstract

We define a set of 2 n驴1驴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.