Entanglement Distillation from Greenberger–Horne–Zeilinger Shares

Vrana, Péter and Christandl, M. (2017) Entanglement Distillation from Greenberger–Horne–Zeilinger Shares. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 352 (2). pp. 621-627. ISSN 0010-3616

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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. © 2017, Springer-Verlag Berlin Heidelberg.

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