Trace-invariants of colored graphs fully label LU orbits of HT multipartite states, completely characterize their LO preorder via weight-function divisibility, and yield large-N combinatorial distinctions from Haar-random states.
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. 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. This generalizes a result by Strassen on the asymptotic subrank of the matrix multiplication tensor.
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Tensor invariants for multipartite entanglement classification
Trace-invariants of colored graphs fully label LU orbits of HT multipartite states, completely characterize their LO preorder via weight-function divisibility, and yield large-N combinatorial distinctions from Haar-random states.