Quantum Information Processing

, Volume 6, Issue 3, pp 187–195 | Cite as

A Characterization of Global Entanglement

  • 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
Article

We define a set of 2n−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.

Keywords

Meyer–Wallach measure elementary monotones entanglement monotones global entanglement four-qubit state qubit labels 

PACS

03.65.Ud 03.67.Lx 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Peter J. Love
    • 1
    • 2
    • 3
  • Alec Maassen van den Brink
    • 2
    • 4
  • A. Yu. Smirnov
    • 2
    • 4
  • M. H. S. Amin
    • 2
  • M. Grajcar
    • 4
    • 5
    • 6
  • E. Il’ichev
    • 5
  • A. Izmalkov
    • 5
  • A. M. Zagoskin
    • 4
    • 7
  1. 1.Department of PhysicsHaverford CollegeHaverfordUSA
  2. 2.D-Wave Systems Inc.BurnabyCanada
  3. 3.Department of MathematicsTufts UniversityMedfordUSA
  4. 4.Frontier Research SystemRIKENWako-shi, SaitamaJapan
  5. 5.Institute for Physical High TechnologyJenaGermany
  6. 6.Department of Solid State PhysicsComenius UniversityBratislavaSlovakia
  7. 7.Physics and Astronomy Dept.The University of British ColumbiaVancouverCanada

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