Quantum Information Processing, Vol. 5, No. 4, August 2006 (© 2006)
On Tight Multiparty Bell Inequalities for Many
Received December 5, 2005; accepted December 7, 2005; Published online April 22, 2006
A derivation method is given, which leads to a series of tight Bell inequalities for
experiments involving N parties, with binary observables, and three possible local
settings. The approach can be generalized to more settings. Ramiﬁcations are
KEY WORDS: Bell inequalities; quantum mechanics; local realism; multiqubit
This paper is not devoted to the meaning and ramiﬁcations of Bell’s
theorem. Rather, it will study some technical aspects associated with mul-
tiparty Bell inequalities. Multiparty Bell inequalities are recently gaining in
importance, because security, or performance, of many of quantum com-
munication schemes (like multiparty key (secret) sharing,
munication complexity problems
) can be measured with Bell inequalities
of some form.
Bell inequalities show the limit of achievable correlations
between many parties, if they share only classical means of communica-
tion and/or computation. If violated by certain predictions for a certain
entangled state, they show that this state, without any further manipula-
tions is a good resource for some quantum informational tasks. To put
it short, in the standard context Bell inequalities show that if there are
QUPON/QIPC Special Issue.
ur Experimentalphysik, Universit
at Wien, Boltzmanngasse 5, A-1090, Wien, Austria.
Instytut Fizyki Teoretycznej i Astroﬁzyki Uniwersytet Gda
nski, PL-80-952 Gda
Tsinghua University, Beijing, China. E-mail: marek. email@example.com
1570-0755/06/0800-0287/0 © 2006 Springer Science+Business Media, Inc.