Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states

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Hayashi, Masahito and Markham, Damian and Murao, Mio and Owari, Masaki and Virmani, Shashank (2008) Entanglement of multiparty-stabilizer, symmetric, and antisymmetric states. Physical Review A, 77 (1). 012104. ISSN 1050-2947 (https://doi.org/10.1103/PhysRevA.77.012104)

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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.

  • Item type:Article
    ID code:16841
    Dates:
    Date
    Event
    2008
    Published
    15 January 2008
    Published Online
    Subjects:Science > Physics > Optics. Light
    Department:Faculty of Science > Physics
    Depositing user: Mr Timothy Briggs
    Date deposited:18 Mar 2010 10:55
    Last modified:12 Dec 2024 02:24
    URI:https://strathprints.strath.ac.uk/id/eprint/16841
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