License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2014.7
URN: urn:nbn:de:0030-drops-48025
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4802/
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Brassard, Gilles ; Devroye, Luc ; Gravel, Claude

Exact Classical Simulation of the GHZ Distribution

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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.

BibTeX - Entry

@InProceedings{brassard_et_al:LIPIcs:2014:4802,
  author =	{Gilles Brassard and Luc Devroye and Claude Gravel},
  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 =	{Steven T. Flammia and Aram W. Harrow},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4802},
  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}
}

Keywords: Entanglement simulation, Greenberger-Horne-Zeilinger (GHZ) state, Multiparty entanglement, von Neumann's rejection algorithm, Knuth-Yao's sampling alg
Collection: 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)
Issue Date: 2014
Date of publication: 11.12.2014

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