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DOI: 10.4230/LIPIcs.TQC.2014.7

Exact Classical Simulation of the GHZ Distribution

Authors: Gilles Brassard, Luc Devroye, and Claude Gravel

Published in: LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

Abstract

John Bell has shown that the correlations entailed by quantum mechanics cannot be reproduced by a classical process involving non-communicating parties. But can they be simulated with the help of bounded communication? This problem has been studied for more than twenty years and it is now well understood in the case of bipartite entanglement. However, the issue was still widely open for multipartite entanglement, even for the simplest case, which is the tripartite Greenberger-Horne-Zeilinger (GHZ) state. We give an exact simulation of arbitrary independent von Neumann measurements on general n-partite GHZ states. Our protocol requires O(n^2) bits of expected communication between the parties, and O(n*log(n)) expected time is sufficient to carry it out in parallel. Furthermore, we need only an expectation of O(n) independent unbiased random bits, with no need for the generation of continuous real random variables nor prior shared random variables. In the case of equatorial measurements, we improve earlier results with a protocol that needs only O(n*log(n)) bits of communication and O(log^2(n)) parallel time. At the cost of a slight increase in the number of bits communicated, these tasks can be accomplished with a constant expected number of rounds.

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Gilles Brassard, Luc Devroye, and Claude Gravel. Exact Classical Simulation of the GHZ Distribution. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 7-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{brassard_et_al:LIPIcs.TQC.2014.7,
  author =	{Brassard, Gilles and Devroye, Luc and Gravel, Claude},
  title =	{{Exact Classical Simulation of the GHZ Distribution}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{7--23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-73-6},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{27},
  editor =	{Flammia, Steven T. and Harrow, Aram W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.7},
  URN =		{urn:nbn:de:0030-drops-48025},
  doi =		{10.4230/LIPIcs.TQC.2014.7},
  annote =	{Keywords: Entanglement simulation, Greenberger-Horne-Zeilinger (GHZ) state, Multiparty entanglement, von Neumann's rejection algorithm, Knuth-Yao's sampling alg}
}

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Exact Classical Simulation of the GHZ Distribution

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