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Entanglement Distillation from Greenberger–Horne–Zeilinger Shares

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Abstract

We study the problem of converting a product of Greenberger–Horne–Zeilinger (GHZ) states shared by subsets of several parties in an arbitrary way into GHZ states shared by every party. Such a state can be described by a hypergraph on the parties as vertices and with each hyperedge corresponding to a GHZ state shared among the parties incident with it. Our result is that if SLOCC transformations are allowed, then the best asymptotic rate is the minimum of bipartite log-ranks of the initial state, which in turn equals the minimum cut of the hypergraph. This generalizes a result by Strassen on the asymptotic subrank of the matrix multiplication tensor.

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Authors and Affiliations

  1. Department of Geometry, Budapest University of Technology and Economics, Egry József u. 1., Budapest, 1111, Hungary

    Péter Vrana

  2. QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Matthias Christandl

Authors
  1. Péter Vrana
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  2. Matthias Christandl
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Correspondence to Péter Vrana.

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Communicated by M. M. Wolf

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Vrana, P., Christandl, M. Entanglement Distillation from Greenberger–Horne–Zeilinger Shares. Commun. Math. Phys. 352, 621–627 (2017). https://doi.org/10.1007/s00220-017-2861-6

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  • DOI: https://doi.org/10.1007/s00220-017-2861-6

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