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arXiv:1112.4502 · Physical Review A

Bilocal versus nonbilocal correlations in entanglement-swapping experiments

Cyril Branciard, Denis Rosset, Nicolas Gisin, Stefano Pironio

Published Mar 19, 2012• 257 citations
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Abstract

Entanglement swapping is a process by which two initially independent quantum systems can become entangled and generate nonlocal correlations. To characterize such correlations, we compare them to those predicted by bilocal models, where systems that are initially independent are described by uncorrelated states. We extend in this paper the analysis of bilocal correlations initiated in [Phys. Rev. Lett. 104, 170401 (2010)]. In particular, we derive new Bell-type inequalities based on the bilocality assumption in different scenarios, we study their possible quantum violations, and we analyze their resistance to experimental imperfections. The bilocality assumption, being stronger than Bell's standard local causality assumption, lowers the requirements for the demonstration of quantumness in entanglement-swapping experiments.

DOI
10.1103/physreva.85.032119

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Entanglement swapping is a process by which two initially independent quantum systems can become entangled and generate nonlocal correlations. To characterize such correlations, we compare them to those predicted by bilocal models, where systems that are initially independent are described by uncorrelated states. We extend in this paper the analysis of bilocal correlations initiated in [Phys. Rev. Lett. 104, 170401 (2010)]. In particular, we derive new Bell-type inequalities based on the bilocality assumption in different scenarios, we study their possible quantum violations, and we analyze their resistance to experimental imperfections. The bilocality assumption, being stronger than Bell's standard local causality assumption, lowers the requirements for the demonstration of quantumness in entanglement-swapping experiments.
Quantum systems that have never interacted can become nonlocally correlated through a process called entanglement swapping. To characterize nonlocality in this context, we introduce local models where quantum systems that are initially uncorrelated are described by uncorrelated local variables. This additional assumption leads to stronger tests of nonlocality. We show, in particular, that an entangled pair generated through entanglement swapping will already violate a Bell-type inequality for visibilities as low as 50% under our assumption.
Quantum mechanics admits correlations that cannot be explained by local realistic models. The most studied models are the standard local hidden variable models, which satisfy the well-known Bell inequalities. To date, most works have focused on bipartite entangled systems. We consider correlations between three parties connected via two independent entangled states. We investigate the new type of so-called "bilocal" models, which correspondingly involve two independent hidden variables. These models describe scenarios that naturally arise in quantum networks, where several independent entanglement sources are used. Using photonic qubits, we build such a linear three-node quantum network and demonstrate nonbilocal correlations by violating a Bell-like inequality tailored for bilocal models. Furthermore, we show that the demonstration of nonbilocality is more noise-tolerant than that of standard Bell nonlocality in our three-party quantum network.
Branciard et al. [Phys. Rev. Lett. 104, 170401 (2010)] first characterized the correlations arising in an entanglement swapping network under the assumption that the sources generating the initially uncorrelated quantum systems are independent. Precisely speaking, Branciard et al. [Phys. Rev. Lett. 104, 170401 (2010) and later in Phys. Rev. A 85, 032119 (2012)] analyzed the importance of bilocal (source independence) assumption to lower the restrictions over correlations for revealing quantumness in the network where each of two sources generates a bipartite entangled state. In this context, one may find interest to characterize correlations in a network involving independent sources which can correlate more than two initially uncorrelated multipartite entangled quantum systems. Our present topic of discussion basically analyzes such a network scenario. Specifically, we introduce a trilocal network scenario where each of three sources independently generates a tripartite entangled quantum system, thereby exploring the role of source independence assumption to exploit nonlocality in a network involving multipartite entanglement analogous to bilocal assumption in a network where only bipartite entanglement was considered. Interestingly, genuine entanglement content did not turn out to be an essential requirement for exploiting nonlocality in such a scenario. Moreover, it is interesting to explore whether such a scenario can be generalized so as to characterize correlations arising in a network involving nnn number of nnn-partite systems for any finite value of $n\ensuremath{\ge}4$ under source independence assumption.
Nonclassical correlations arising in complex quantum networks are attracting growing interest, both from a fundamental perspective and for potential applications in information processing. In particular, in an entanglement swapping scenario a new kind of correlations arise, the so-called nonbilocal correlations that are incompatible with local realism augmented with the assumption that the sources of states used in the experiment are independent. In practice, however, bilocality tests impose strict constraints on the experimental setup and in particular to the presence of shared reference frames between the parties. Here, we experimentally address this point showing that false positive nonbilocal quantum correlations can be observed even though the sources of states are independent. To overcome this problem, we propose and demonstrate a scheme for the violation of bilocality that does not require shared reference frames and thus constitutes an important building block for future investigations of quantum correlations in complex networks.
Nonlocality arising in networks composed of several independent sources gives rise to phenomena radically different from that in standard Bell scenarios. Over the years, the phenomenon of network nonlocality in the entanglement-swapping scenario has been well investigated and demonstrated. However, it is known that violations of the so-called bilocality inequality used in previous experimental demonstrations cannot be used to certify the nonclassicality of their sources. This has put forward a stronger concept for nonlocality in networks, called full network nonlocality. Here, we experimentally observe full network nonlocal correlations in a network where the source-independence, locality, and measurement-independence loopholes are closed. This is ensured by employing two independent sources, rapid setting generation, and spacelike separations of relevant events. Our experiment violates known inequalities characterizing nonfull network nonlocal correlations by over 5 standard deviations, certifying the absence of classical sources in the realization.
The concept of bilocality was introduced to study the correlations which arise in an entanglement-swapping scenario, where one has two sources which can naturally be taken to be independent. This additional constraint leads to stricter requirements than simply imposing locality, in the form of bilocality inequalities. In this work we consider a natural generalization of the bilocality scenario; namely, the star network consisting of a single central party surrounded by nnn edge parties, each of which shares an independent source with the center. We derive inequalities which are satisfied by all local correlations in this scenario, for the cases when the central party performs (i) two dichotomic measurements (ii) a single Bell-state measurement. We demonstrate quantum violations of these inequalities and study both the robustness to noise and to losses.