Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states

Masahito Hayashi, Damian Markham, Mio Murao, Masaki Owari, Shashank Virmani

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Abstract

We study various distance-like entanglement measures of multipartite states under certain symmetries. Using group averaging techniques we provide conditions under which the relative entropy of entanglement, the geometric measure of entanglement and the logarithmic robustness are equivalent. We consider important classes of multiparty states, and in particular show that these measures are equivalent for all stabilizer states, symmetric basis and antisymmetric basis states. We rigorously prove a conjecture that the closest product state of permutation symmetric states can always be chosen to be permutation symmetric. This allows us to calculate the explicit values of various entanglement measures for symmetric and antisymmetric basis states, observing that antisymmetric states are generally more entangled. We use these results to obtain a variety of interesting ensembles of quantum states for which the optimal LOCC discrimination probability may be explicitly determined and achieved. We also discuss applications to the construction of optimal entanglement witnesses.
Original languageEnglish
Article number012104
Number of pages15
JournalPhysical Review A
Volume77
Issue number1
Early online date15 Jan 2008
DOIs
Publication statusPublished - 2008

Keywords

  • quantum states
  • purification
  • channels
  • antisymmetric states
  • physics

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