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

arXiv:quant-ph/0206165 · Physical Review A

Functional Bell inequalities can serve as a stronger entanglement witness than conventional Bell inequalities

Aditi Sen, Ujjwal Sen, Marek Żukowski

Published Dec 30, 2002• 26 citations
arXivHTMLPDF

Abstract

We consider a Bell inequality for a continuous range of settings of the apparatus at each site. This ``functional'' Bell inequality gives a better range of violation for generalized Greenberger, Horne, and Zeilinger states. Also a family of N-qubit bound entangled states violate this inequality for $N>5.$

DOI
10.1103/physreva.66.062318

Related papers

Variant of the Clauser-Horne-Shimony-Holt inequality

Zeqian Chen

We construct a Bell inequality from the Clauser-Horne-Shimony-Holt inequality for two qubits that provides a stronger bound on the correlations of entangled states than allowed by the CHSH inequality. The argument involved here can be generalized to $n$ qubits. The inequalities obtained are violated by all the generalized Greenberger-Horne-Zeilinger states of multiqubits.

arXiv:0711.0810•Nov 6, 2007•0 citations

Variants of Bell inequalities

Zeqian Chen

A family of Bell-type inequalities is present, which are constructed directly from the "standard" Bell inequalities involving two dichotomic observables per site. It is shown that the inequalities are violated by all the generalized Greenberger-Horne-Zeilinger states of multiqubits. Remarkably, our new inequalities can provide stronger non-locality tests in a sense that the local reality inequalities are exponentially stronger than the corresponding multipartite separability inequalities. This reveals that the exponential violation of local realism by separable states is an interesting consequence of quantum fluctuation of multipartite systems.

arXiv:quant-ph/0611126•Nov 13, 2006•0 citations

Multipartite bound entanglement and multisetting Bell inequalities

Dong Pyo Chi, Kabgyun Jeong, Tae‐Wan Kim +2 more

D\"ur [Phys. Rev. Lett. 87, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $N\ensuremath{\ge}8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled state violating the same Bell inequality if and only if $N\ensuremath{\ge}6$ [Phys. Rev. A 79, 032309 (2009)]. On the other hand, it has been also shown that the states which D\"ur considered violate Bell inequalities different from the inequality for $N\ensuremath{\ge}6$. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities with $M$ settings of the measuring apparatus for sufficiently large $M$, we prove that there exists an $N$-qubit bound entangled state violating the $M$-setting Bell inequality if and only if $N\ensuremath{\ge}4$.

arXiv:0904.4818•Physical Review A•Sep 28, 2009•3 citations

Testing the Structure of Multipartite Entanglement with Bell Inequalities

Nicolas Brunner, James Sharam, Tamás Vértesi

We show that the rich structure of multipartite entanglement can be tested following a device-independent approach. Specifically we present Bell inequalities for distinguishing between different types of multipartite entanglement, without placing any assumptions on the measurement devices used in the protocol, in contrast with usual entanglement witnesses. We first address the case of three qubits and present Bell inequalities that can be violated by W states but not by Greenberger-Horne-Zeilinger states, and vice versa. Next, we devise 'subcorrelation Bell inequalities' for any number of parties, which can provably not be violated by a broad class of multipartite entangled states (generalizations of Greenberger-Horne-Zeilinger states), but for which violations can be obtained for W states. Our results give insight into the nonlocality of W states. The simplicity and robustness of our tests make them appealing for experiments.

arXiv:1110.5512•Physical Review Letters•Mar 12, 2012•91 citations

Multipartite bound entanglement and three-setting Bell inequalities

Dagomir Kaszlikowski, L. C. Kwek, Jing‐Ling Chen +1 more

It was shown by Dur [Phys. Rev. Lett. $87,$ 230402 (2001)] that N $(N>~4)$ qubits described by a certain one-parameter family $\mathcal{F}$ of bound entangled states violate the Mermin-Klyshko inequality for $N>~8.$ In this paper we prove that the states from the family $\mathcal{F}$ violate Bell inequalities derived by \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski and Kaszlikowski [Phys. Rev. A $56,$ R1682 (1997)], in which each observer measures three noncommuting sets of orthogonal projectors, for $N>~7.$ We also derive a simple one-parameter family of entanglement witnesses that detect entanglement for all the states belonging to $\mathcal{F}.$ It is possible that these entanglement witnesses could be generated by some Bell inequalities.

arXiv:quant-ph/0206031•Physical Review A•Nov 18, 2002•23 citations

Distribution of Bell-inequality violation versus multiparty-quantum-correlation measures

Kunal Sharma, Tamoghna Das, Aditi Sen +1 more

Violation of a Bell inequality guarantees the existence of quantum correlations in a shared quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states in the case of multipartite correlation function Bell inequalities with two settings at each site. We establish a connection between the monogamy of Bell-inequality violation and multiparty quantum correlations for shared multisite quantum states. We believe that the relation is generic, as it is true for a number of different multisite measures that are defined from radically different perspectives. Precisely, we quantify the multisite-quantum-correlation content in the states by generalized geometric measure, a genuine multisite entanglement measure, as well as three monogamy-based multiparty-quantum-correlation measures, viz., 3-tangle, quantum-discord score, and quantum-work-deficit score. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family of states, which we refer to as the special Greenberger-Horne-Zeilinger states, have the status of extremal states in such relations.

arXiv:1512.01477•Physical Review A•Jun 28, 2016•7 citations
We consider a Bell inequality for a continuous range of settings of the apparatus at each site. This ``functional'' Bell inequality gives a better range of violation for generalized Greenberger, Horne, and Zeilinger states. Also a family of N-qubit bound entangled states violate this inequality for N>5.N>5.N>5.
We construct a Bell inequality from the Clauser-Horne-Shimony-Holt inequality for two qubits that provides a stronger bound on the correlations of entangled states than allowed by the CHSH inequality. The argument involved here can be generalized to nnn qubits. The inequalities obtained are violated by all the generalized Greenberger-Horne-Zeilinger states of multiqubits.
A family of Bell-type inequalities is present, which are constructed directly from the "standard" Bell inequalities involving two dichotomic observables per site. It is shown that the inequalities are violated by all the generalized Greenberger-Horne-Zeilinger states of multiqubits. Remarkably, our new inequalities can provide stronger non-locality tests in a sense that the local reality inequalities are exponentially stronger than the corresponding multipartite separability inequalities. This reveals that the exponential violation of local realism by separable states is an interesting consequence of quantum fluctuation of multipartite systems.
D\"ur [Phys. Rev. Lett. 87, 230402 (2001)] constructed NNN-qubit bound entangled states which violate a Bell inequality for $N\ensuremath{\ge}8$, and his result was recently improved by showing that there exists an NNN-qubit bound entangled state violating the same Bell inequality if and only if $N\ensuremath{\ge}6$ [Phys. Rev. A 79, 032309 (2009)]. On the other hand, it has been also shown that the states which D\"ur considered violate Bell inequalities different from the inequality for $N\ensuremath{\ge}6$. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities with MMM settings of the measuring apparatus for sufficiently large MMM, we prove that there exists an NNN-qubit bound entangled state violating the MMM-setting Bell inequality if and only if $N\ensuremath{\ge}4$.
We show that the rich structure of multipartite entanglement can be tested following a device-independent approach. Specifically we present Bell inequalities for distinguishing between different types of multipartite entanglement, without placing any assumptions on the measurement devices used in the protocol, in contrast with usual entanglement witnesses. We first address the case of three qubits and present Bell inequalities that can be violated by W states but not by Greenberger-Horne-Zeilinger states, and vice versa. Next, we devise 'subcorrelation Bell inequalities' for any number of parties, which can provably not be violated by a broad class of multipartite entangled states (generalizations of Greenberger-Horne-Zeilinger states), but for which violations can be obtained for W states. Our results give insight into the nonlocality of W states. The simplicity and robustness of our tests make them appealing for experiments.
It was shown by Dur [Phys. Rev. Lett. 87,87,87, 230402 (2001)] that N (N> 4)(N>~4)(N> 4) qubits described by a certain one-parameter family F\mathcal{F}F of bound entangled states violate the Mermin-Klyshko inequality for N> 8.N>~8.N> 8. In this paper we prove that the states from the family F\mathcal{F}F violate Bell inequalities derived by \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski and Kaszlikowski [Phys. Rev. A 56,56,56, R1682 (1997)], in which each observer measures three noncommuting sets of orthogonal projectors, for N> 7.N>~7.N> 7. We also derive a simple one-parameter family of entanglement witnesses that detect entanglement for all the states belonging to F.\mathcal{F}.F. It is possible that these entanglement witnesses could be generated by some Bell inequalities.
Violation of a Bell inequality guarantees the existence of quantum correlations in a shared quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states in the case of multipartite correlation function Bell inequalities with two settings at each site. We establish a connection between the monogamy of Bell-inequality violation and multiparty quantum correlations for shared multisite quantum states. We believe that the relation is generic, as it is true for a number of different multisite measures that are defined from radically different perspectives. Precisely, we quantify the multisite-quantum-correlation content in the states by generalized geometric measure, a genuine multisite entanglement measure, as well as three monogamy-based multiparty-quantum-correlation measures, viz., 3-tangle, quantum-discord score, and quantum-work-deficit score. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family of states, which we refer to as the special Greenberger-Horne-Zeilinger states, have the status of extremal states in such relations.