Geometric Entanglement of Symmetric States and the Majorana Representation

  • Martin Aulbach
  • Damian Markham
  • Mio Murao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6519)

Abstract

Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12 (2010) 073025], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-based quantum computing is also discussed.

Keywords

Majorana representation geometric measure symmetric entanglement anticoherent spherical design 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin Aulbach
    • 1
    • 2
  • Damian Markham
    • 3
  • Mio Murao
    • 4
    • 5
  1. 1.The School of Physics and AstronomyUniversity of LeedsLeedsUnited Kingdom
  2. 2.Clarendon Laboratory, Department of PhysicsUniversity of OxfordOxfordUnited Kingdom
  3. 3.CNRS, LTCI, Telecom ParisTechParisFrance
  4. 4.Department of Physics, Graduate School of ScienceThe University of TokyoTokyoJapan
  5. 5.Institute for Nano Quantum Information ElectronicsThe University of TokyoTokyoJapan

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