Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states

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

Research output: Contribution to journalArticle

60 Citations (Scopus)

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.
LanguageEnglish
Article number012104
Number of pages15
JournalPhysical Review A
Volume77
Issue number1
Early online date15 Jan 2008
DOIs
Publication statusPublished - 2008

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permutations
discrimination
entropy
symmetry
products

Keywords

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

Cite this

Hayashi, M., Markham, D., Murao, M., Owari, M., & Virmani, S. (2008). Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states. Physical Review A, 77(1), [012104]. https://doi.org/10.1103/PhysRevA.77.012104
Hayashi, Masahito ; Markham, Damian ; Murao, Mio ; Owari, Masaki ; Virmani, Shashank. / Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states. In: Physical Review A. 2008 ; Vol. 77, No. 1.
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Hayashi, M, Markham, D, Murao, M, Owari, M & Virmani, S 2008, 'Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states' Physical Review A, vol. 77, no. 1, 012104. https://doi.org/10.1103/PhysRevA.77.012104

Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states. / Hayashi, Masahito; Markham, Damian; Murao, Mio; Owari, Masaki; Virmani, Shashank.

In: Physical Review A, Vol. 77, No. 1, 012104, 2008.

Research output: Contribution to journalArticle

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