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

Physical Review A

Multipartite nonlocality distillation

Li‐Yi Hsu, Keng-Shuo Wu

Published Nov 1, 2010• 13 citations
Publisher

Abstract

The stronger nonlocality than that allowed in quantum theory can provide an advantage in information processing and computation. Since quantum entanglement is distillable, can nonlocality be distilled in the nonsignalling condition? The answer is positive in the bipartite case. In this article the distillability of the multipartite nonlocality is investigated. We propose a distillation protocol solely exploiting xor operations on output bits. The probability-distribution vectors and matrix are introduced to tackle the correlators. It is shown that only the correlators with extreme values can survive the distillation process. As the main result, the amplified nonlocality cannot maximally violate any Bell-type inequality. Accordingly, a distillability criterion in the postquantum region is proposed.

DOI
10.1103/physreva.82.052102

Related papers

Distilling Nonlocality

Manuel Förster, Severin Winkler, Stefan Wolf

Two parts of an entangled quantum state can have a correlation, in their joint behavior under measurements, that is unexplainable by shared classical information. Such correlations are called nonlocal and have proven to be an interesting resource for information processing. Since nonlocal correlations are more useful if they are stronger, it is natural to ask whether weak nonlocality can be amplified. We give an affirmative answer by presenting the first protocol for distilling nonlocality in the framework of generalized nonsignaling theories. Our protocol works for both quantum and nonquantum correlations. This shows that in many contexts, the extent to which a single instance of a correlation can violate a Clauser-Horne-Shimony-Holt inequality is not a good measure for the usefulness of nonlocality. A more meaningful measure follows from our results.

arXiv:0809.3173•Physical Review Letters•Mar 24, 2009•82 citations

Nonlocality Distillation for High-Dimensional System

Guo‐Zhu Pan, Chao Li, Zheng-Gen Chen +2 more

The intriguing and powerful capability of nonlocality in communication field ignites the research of the nonlocality distillation. The first protocol presented in Ref[Phys. Rev. Lett. 102, 120401] shows that the nonlocality of bipartite binary-input and binary-output nonsignaling correlated boxes could be amplified by 'wiring' two copies of weaker-nonlocality boxes. Several optimized distillation protocols were presented later for bipartite binary-input and binary-output nonsignaling correlated boxes. In this paper, we focus on the bipartite binary-input and multi-nary-output nonsignaling correlated boxes---high-dimensional boxes, and design comparators-based protocols to achieve the distillation of high-dimensional nonlocality. The results show that the high-dimensional nonlocality can be distilled in different ways, and we find that the efficiencies of the protocols are influenced not only by the wirings but also by the classes the initial nonlocality boxes belongs to. Here, the initial nonlcalities may have the same violation of the high-dimensional Bell-type inequality, but they can fall into different classes, which shows that the value of the violation of the high-dimensional Bell-type inequality is not the only representation of nonlocality, and the combination manner(classes) in the expression of the correlated boxes is another important nonlocal representation too. The current protocols are compatible with the previous two-dimensional nonlocality distillation protocols, but our protocols are more powerful and universal than previous ones in the sense that the current protocols can be applied to the system with any dimension rather than the only two-dimension system in the previous protocols.

arXiv:1202.4054•Feb 18, 2012•0 citations

Quantum Nonlocality Does Not Imply Entanglement Distillability

Tamás Vértesi, Nicolas Brunner

Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is, however, still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a long-standing conjecture made by Peres.

arXiv:1106.4850•Physical Review Letters•Jan 19, 2012•89 citations

Disproving the Peres conjecture: nonlocality does not imply entanglement distillability

Tamás Vértesi, Nicolas Brunner

Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is however still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a longstanding conjecture made by Asher Peres.

•Jun 23, 2011•0 citations

Asymptotic Violation of Bell Inequalities and Distillability

Lluís Masanes

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.

arXiv:quant-ph/0512153•Physical Review Letters•Aug 3, 2006•118 citations

Bell’s inequalities and distillability inN-quantum-bit systems

Antonio Acín, Valerio Scarani, Michael M. Wolf

The relation between Bell's inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficient for full N-partite distillability. This result also allows for a security proof of multipartite quantum key distribution protocols.

arXiv:quant-ph/0206084•Physical Review A•Oct 25, 2002•34 citations
The stronger nonlocality than that allowed in quantum theory can provide an advantage in information processing and computation. Since quantum entanglement is distillable, can nonlocality be distilled in the nonsignalling condition? The answer is positive in the bipartite case. In this article the distillability of the multipartite nonlocality is investigated. We propose a distillation protocol solely exploiting xor operations on output bits. The probability-distribution vectors and matrix are introduced to tackle the correlators. It is shown that only the correlators with extreme values can survive the distillation process. As the main result, the amplified nonlocality cannot maximally violate any Bell-type inequality. Accordingly, a distillability criterion in the postquantum region is proposed.
Two parts of an entangled quantum state can have a correlation, in their joint behavior under measurements, that is unexplainable by shared classical information. Such correlations are called nonlocal and have proven to be an interesting resource for information processing. Since nonlocal correlations are more useful if they are stronger, it is natural to ask whether weak nonlocality can be amplified. We give an affirmative answer by presenting the first protocol for distilling nonlocality in the framework of generalized nonsignaling theories. Our protocol works for both quantum and nonquantum correlations. This shows that in many contexts, the extent to which a single instance of a correlation can violate a Clauser-Horne-Shimony-Holt inequality is not a good measure for the usefulness of nonlocality. A more meaningful measure follows from our results.
The intriguing and powerful capability of nonlocality in communication field ignites the research of the nonlocality distillation. The first protocol presented in Ref[Phys. Rev. Lett. 102, 120401] shows that the nonlocality of bipartite binary-input and binary-output nonsignaling correlated boxes could be amplified by 'wiring' two copies of weaker-nonlocality boxes. Several optimized distillation protocols were presented later for bipartite binary-input and binary-output nonsignaling correlated boxes. In this paper, we focus on the bipartite binary-input and multi-nary-output nonsignaling correlated boxes---high-dimensional boxes, and design comparators-based protocols to achieve the distillation of high-dimensional nonlocality. The results show that the high-dimensional nonlocality can be distilled in different ways, and we find that the efficiencies of the protocols are influenced not only by the wirings but also by the classes the initial nonlocality boxes belongs to. Here, the initial nonlcalities may have the same violation of the high-dimensional Bell-type inequality, but they can fall into different classes, which shows that the value of the violation of the high-dimensional Bell-type inequality is not the only representation of nonlocality, and the combination manner(classes) in the expression of the correlated boxes is another important nonlocal representation too. The current protocols are compatible with the previous two-dimensional nonlocality distillation protocols, but our protocols are more powerful and universal than previous ones in the sense that the current protocols can be applied to the system with any dimension rather than the only two-dimension system in the previous protocols.
Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is, however, still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a long-standing conjecture made by Peres.
Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is however still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a longstanding conjecture made by Asher Peres.
A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.
The relation between Bell's inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficient for full N-partite distillability. This result also allows for a security proof of multipartite quantum key distribution protocols.