Quantum networks, which can exceed the framework of standard bell theorem, flourish the investigation of quantum nonlocality further. Recently, a concept of full quantum network nonlocality (FNN) which is stronger than network nonlocality, has been defined and can be witnessed by Kerstjens-Gisin-Tavakoli (KGT) inequalities [Phys. Rev. Lett. 128 (2022)]. In this letter, we explored the recycling of FNN as quantum resources by analyzing the FNN sharing between different combinations of observers. The FNN sharing in extended bilocal scenario via weak measurements has been completely discussed. According to the different motivations of the observer-Charlie1, two types of possible FNN sharing, passive FNN sharing and active FNN sharing, can be investigated by checking the simultaneous violation of KGT inequalities between Alice-Bob-Charlie1 and Alice-Bob- Charlie2. Our results show that passive FNN sharing is impossible while active FNN sharing can be achieved by proper measurements, which indicate that FNN sharing requires more cooperation by the intermediate observers compared with Bell nonlocal sharing and network nonlocal sharing.
Networks have advanced the study of nonlocality beyond Bell's theorem. Here, we introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. Showcasing that this notion is stronger than standard network nonlocality, we prove that the most well-known network Bell test does not witness full network nonlocality. In contrast, we demonstrate that its generalization to star networks is capable of detecting full network nonlocality in quantum theory. More generally, we point out that established methods for analyzing local and theory-independent correlations in networks can be combined in order to systematically deduce sufficient conditions for full network nonlocality in any network and input-output scenario. We demonstrate the usefulness of these methods by constructing polynomial witnesses of full network nonlocality for the bilocal scenario. Then, we show that these inequalities can be violated via quantum elegant joint measurements.
Network nonlocality exhibits completely novel quantum correlations compared to standard quantum nonlocality. It has been shown that network nonlocality can be shared in a generalized bilocal scenario via weak measurements [Hou, Liu, and Ren, Phys. Rev. A 105, 042436 (2022)]. In this paper, we investigate network nonlocality sharing via weak measurements in a generalized star-shaped network configuration with arbitrary numbers of unbiased dichotomic input
k, which includes
n branches and adds $(m\ensuremath{-}1)$ more parties in each branch to the original star network
(n,m=1,k=2) scenario. It is shown that network nonlocality sharing among all observers can be revealed from simultaneous violation of
2n inequalities in the
(n,m=2,k=2) and
(n,m=2,k=3) scenarios for any
n branches. The noise resistance of network nonlocality sharing with a precise noise model is also analyzed.
Bell's theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more sophisticated experiments that involve several independent sources which distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.
Network Nonlocality is an advanced study of quantum nonlocality that comprises network structure beyond Bell's theorem. The development of quantum networks has the potential to bring a lot of technological applications in sevaral quantum information processing tasks. Here, we are focusing on how the role of the independence of the measurement choices of the end parties in a network works and can be used to enhance the security in a quantum network. In both three-parties two-sources bilocal network and four-parties three-sources star network scenarios, we are able to show, a practical way to understand the relaxation of the assumptions to enhance a real security protocol if someone wants to breach in a network communications. Theoratically, we have proved that by relaxing the independence of the measurement choices of only one end party we can create a Standard Network Nonlocality(SNN) and more stronger Full Network Nonlocality(FNN) and we can get maximum quantum violation by the classical no-signalling local model. We are able to distinguish between two types of network nonlocality in the sense that the FNN is stronger than SNN, i.e., FNN states all the sources in a network need to distribute nonlocal resources.
Of late, there has been an upsurge of interest in studying the sequential sharing of various forms of quantum correlations, viz., nonlocality, preparation contextuality, coherence, and entanglement. In this work, we explore the sequential sharing of nonlocality in a quantum network. We first consider the simplest case of the two-input bilocality scenario that features two independent sources and three parties, including two edge parties and a central party. We demonstrate that, in the symmetric case when the sharing is considered for both the edge parties, the nonlocality can be shared by, at most, two sequential observers per edge party. However, in the asymmetric case, when the sharing across one edge party is considered, we show that, at most, six sequential observers can share the nonlocality in the network. We extend our investigation to the two-input
n-local scenario in the star-network configuration that features an arbitrary
n number of edge parties and one central party. In the asymmetric case, we demonstrate that the network nonlocality can be shared by an unbounded number of sequential observers across one edge party for a suitably large value of
n. Further, we generalize our study for an arbitrary
m input
n-local scenario in the star-network configuration. We show that, even for an arbitrary
m input scenario, the nonlocality can be shared by an unbounded number of sequential observers. However, increasing the input
m, one has to employ a larger number of edge parties
n than that of the two-input case to demonstrate the sharing of an unbounded number of sequential observers.