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2016

Entanglement distillation from Greenberger-Horne-Zeilinger shares

Vrana, Péter, Christandl, Matthias

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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.

Entanglement distillation from Greenberger-Horne-Zeilinger shares · Around

Built on

V. Strassen, “Relative bilinear complexity and matrix multiplication”, Journal für die reine und angewandte Mathematik (1987) Vol. 375-376, 406-443
1987
Earlier work this paper cites.
L. Lovász, M. Saks, A. Schrijver, “Orthogonal representations and connectivity of graphs”, Linear Alg. Appl. 114/115
1989
Earlier work this paper cites.
V. Strassen, “Degeneration and complexity of bilinear maps: Some asymptotic spectra”, J. Reine Angew. Math. 413 (1991), pp. 127–180
1991
Earlier work this paper cites.

Similar

L. Lovász, M. Saks, A. Schrijver, “A Correction: Orthogonal representations and connectivity of graphs”, Linear Alg. Appl. 313
2000
Cited alongside, same era.
J. A. Smolin, F. Verstraete, and A. Winter, “Entanglement of assistance and multipartite state distillation,” Physical Review A
2005
Cited alongside, same era.
E. Chitambar, R. Duan, Y. Shi, “Tripartite Entanglement Transformations and Tensor Rank”, Phys. Rev. Lett. 101, 140502 (2008)
2008
Cited alongside, same era.
D. Bini, G. Lotti, F. Romani, “Approximate solutions for the bilinear form computational problem”, SIAM J. Comput. , 9(4), 692–697
Cited in the paper.
H. Buhrman, M. Christandl, and J. Zuiddam, Multiparty quantum communication complexity: the cyclic equality game and iterated matrix multiplication , arXiv:1603.03757
Original
Cited in the paper.

Then

F. Le Gall, “Powers of tensors and fast matrix multiplication”. In Proceedings of the 39th international symposium on symbolic and algebraic computation , pages 296–303. ACM, 2014
2014
Later among the works it cites.
P. Vrana and M. Christandl, “Asymptotic entanglement transformation between W and GHZ states,” Journal of Mathematical Physics
2015
Later among the works it cites.

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