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Physical Review A

Nonlocal distillation based on multisetting Bell inequality

Xiang-Jun Ye, Dong-Ling Deng, Jing‐Ling Chen

Published Dec 10, 2012• 6 citations
Publisher

Abstract

Inspired by the recent works of Foster et al. [Phys. Rev. Lett. 102, 120401 (2009)] and Brunner et al. [Phys. Rev. Lett. 102, 160403 (2009)], we present a nonlocality distillation protocol for two three-level (qutrit) systems in the framework of generalized nonsignaling theories. Our protocol is based on a three-setting Bell inequality. It works efficiently for a specific class of three-input--three-output nonlocal boxes. In the asymptotic limit, all these nonlocal boxes can be distilled to the maximally nonlocal box defined by the inequality and nonsignaling constraints. Then we introduce a contracting protocol that reduces these boxes to the so-called ``correlated nonlocal boxes.'' As a result, our three-input--three-output nonlocal boxes also make communication complexity trivial and appear very unlikely to exist in nature.

DOI
10.1103/physreva.86.062103

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Inspired by the recent works of Foster et al. [Phys. Rev. Lett. 102, 120401 (2009)] and Brunner et al. [Phys. Rev. Lett. 102, 160403 (2009)], we present a nonlocality distillation protocol for two three-level (qutrit) systems in the framework of generalized nonsignaling theories. Our protocol is based on a three-setting Bell inequality. It works efficiently for a specific class of three-input--three-output nonlocal boxes. In the asymptotic limit, all these nonlocal boxes can be distilled to the maximally nonlocal box defined by the inequality and nonsignaling constraints. Then we introduce a contracting protocol that reduces these boxes to the so-called ``correlated nonlocal boxes.'' As a result, our three-input--three-output nonlocal boxes also make communication complexity trivial and appear very unlikely to exist in nature.
We first present a protocol for deterministically distilling nonlocality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)10.1103/PhysRevLett.102.120401]. Our protocol, which is optimal for two-copy distillation, works efficiently for a specific class of postquantum nonlocal boxes, which we term correlated nonlocal boxes. In the asymptotic limit, all correlated nonlocal boxes are distilled to the maximally nonlocal box of Popescu and Rohrlich. Then, taking advantage of a result of Brassard et al. [Phys. Rev. Lett. 96, 250401 (2006)10.1103/PhysRevLett.96.250401] we show that all correlated nonlocal boxes make communication complexity trivial, and therefore appear very unlikely to exist in nature. Astonishingly, some of these nonlocal boxes are arbitrarily close to the set of classical correlations. This result therefore gives new insight to the problem of why quantum nonlocality is limited.
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.
We report the first experimental demonstration of distillation of quantum nonlocality, confirming the recent theoretical protocol [Phys. Rev. Lett. 102, 120401 (2009)]. Quantum nonlocality is described by a correlation box with binary inputs and outputs, and the nonlocal boxes are realized through appropriate measurements on polarization entangled photon pairs. We demonstrate that nonlocality is amplified by connecting two nonlocal boxes into a composite one through local operations and four-photon measurements.
Recent advances on nonlocality show that nonlocal correlations in the form of non-signaling correlated boxes can be distilled.The bipartite binary-inputs and binary-outputs non-signaling correlated boxes were widely discussed,and several efficient protocols were presented to distill them.In this paper,we generalize these bipartite distillation protocols to the tripartite cases.We find that the BS protocol(by N.Brunner and P.Skrzypczyk) for bipartite system still works in tripartite cases,but has a less efficiency than in bipartite system.
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.