Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Fortschritte der Physik

On Bell's theorem for N‐qubits

Marek Żukowski, Časlav Brukner

Published Apr 24, 2003• 0 citations
Publisher

Abstract

Abstract We present a single general Bell inequality that summarizes all possible Bell type constrains on the correlation function for the N‐particle system (i.e., it is a necessary and sufficient condition for the existence of local realistic models for the correlation function). It is applicable in the case when measurements on each particle can be chosen between two arbitrary dichotomic observables. We also obtain a necessary and sufficient condition for an arbitrary N‐qubit mixed state to violate this general Bell inequality.

DOI
10.1002/prop.200310071

Related papers

Bell’s Theorem for GeneralN-Qubit States

Marek Żukowski, Časlav Brukner

We derive a single general Bell inequality which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodecki family condition for two qubits.

arXiv:quant-ph/0102039•Physical Review Letters•May 9, 2002•422 citations

Do All Pure Entangled States Violate Bell’s Inequalities for Correlation Functions?

Marek Żukowski, Časlav Brukner, Wiesław Laskowski +1 more

Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.

arXiv:quant-ph/0110095•Physical Review Letters•May 9, 2002•111 citations

Gisin's theorem cannot be generalized to all multi-particle states

Marek Żukowski, Časlav Brukner, Wiesław Laskowski +1 more

Gisin's theorem states that any pure entangled state of two particles violates Clauser-Horne-Shimony-Holt inequality which is a bound on correlations between measurements on two particles obtained within local realistic picture. We find that this theorem cannot be generalized to all multi-particle states for the case where measurements on each particle can be chosen between two arbitrary dichotomic observables. In particular we find a family of pure entangled states of N qubits which do not violate any Bell inequality for correlations between such measurements. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description of correlations.

•Oct 15, 2001•1 citation

All tight multipartite Bell correlation inequalities for an arbitrary number of dichotomic observables per observer

Piotr Badziąg, Marek Żukowski

Derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and N possible local settings is not as easy as it seemed. The proof of v1 is wrong. Additionaly one can find a counterexample, which will be presented soon. Thus our thesis is dead. Still the series of Bell inequalities discussed in the manuscript (v1) form a necessary condition for local realism, and are tight. They are tight and complete (sufficient) only for N=3 settings per observer (as shown in quant-ph/0611086, fortunately using an entirely different approach).

arXiv:0704.1809•Apr 13, 2007•0 citations

Explicit form of correlation-function three-setting tight Bell inequalities for three qubits

Marcin Wieśniak, Piotr Badziąg, Marek Żukowski

We present a method to derive explicit forms of tight correlation-function Bell inequalities for three systems and dichotomic observables, which involve three settings for each observer. We also give sufficient and necessary conditions for quantum predictions to satisfy the new inequalities.

arXiv:quant-ph/0611083•Physical Review A•Jul 16, 2007•18 citations

Collapse of Bell’s Theorem

Guangye Chen

Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.

Journal of Modern Physics•Jan 1, 2019•4 citations
Abstract We present a single general Bell inequality that summarizes all possible Bell type constrains on the correlation function for the N‐particle system (i.e., it is a necessary and sufficient condition for the existence of local realistic models for the correlation function). It is applicable in the case when measurements on each particle can be chosen between two arbitrary dichotomic observables. We also obtain a necessary and sufficient condition for an arbitrary N‐qubit mixed state to violate this general Bell inequality.
We derive a single general Bell inequality which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodecki family condition for two qubits.
Gisin's theorem states that any pure entangled state of two particles violates Clauser-Horne-Shimony-Holt inequality which is a bound on correlations between measurements on two particles obtained within local realistic picture. We find that this theorem cannot be generalized to all multi-particle states for the case where measurements on each particle can be chosen between two arbitrary dichotomic observables. In particular we find a family of pure entangled states of N qubits which do not violate any Bell inequality for correlations between such measurements. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description of correlations.
Derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and N possible local settings is not as easy as it seemed. The proof of v1 is wrong. Additionaly one can find a counterexample, which will be presented soon. Thus our thesis is dead. Still the series of Bell inequalities discussed in the manuscript (v1) form a necessary condition for local realism, and are tight. They are tight and complete (sufficient) only for N=3 settings per observer (as shown in quant-ph/0611086, fortunately using an entirely different approach).
Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.