The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as the quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question as to how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce an approach to prove the generic activated nonlocality as a result of entanglement swapping for all the bipartite entangled states. The result is further applied to show the multipartite nonlocality and activated nonlocality for all the nontrivial quantum networks consisting of any entangled states. Our results provide the nonlocality witnesses and quantum superiorities of all the connected quantum networks or nontrivial hybrid networks in contrast to classical networks.
The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as the quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question as to how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce an approach to prove the generic activated nonlocality as a result of entanglement swapping for all the bipartite entangled states. The result is further applied to show the multipartite nonlocality and activated nonlocality for all the nontrivial quantum networks consisting of any entangled states. Our results provide the nonlocality witnesses and quantum superiorities of all the connected quantum networks or nontrivial hybrid networks in contrast to classical networks.
As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many parties. We apply it to study the tripartite scenario in detail, where we fully characterize all the nonlocality classes. Remarkably, we identify new highly nonlocal causal structures that cannot reproduce all quantum correlations. This shows, to our knowledge, the strongest form of quantum multipartite nonlocality known to date. Finally, as a by-product result, we derive a non-trivial Bell-type inequality with no quantum violation. Our findings constitute a significant step forward in the understanding of multipartite Bell nonlocality and open several venues for future research.
Despite the success of quantum mechanics in predicting the outcomes of experiments in many branches of physics, the foundations of the theory have remained subject of research and dispute. At the basis of this struggle with the theory lie the phenomena of nonlocality and entanglement. Since it was first predicted by Bell in 1964, nonlocality was not only verified in numerous experiments, but also identified as a useful resource for quantum information processing. Thus, the study of nonlocality is important both from a fundamental point of view and with respect to new applications in quantum information theory, such as secure cryptography and randomness generation. The identification of entanglement as a resource for quantum information led to a strong theoretical effort devoted to its characterisation and detection. Many of the resulting mathematical tools find application in several domains of physics. Although the only known way to create nonlocal correlations is to measure entangled quantum systems, it has been shown that entanglement and nonlocality constitute two inequivalent properties. Therefore, in the light of the success of entanglement theory, it is of interest to also devise a resource theory of nonlocality. The task of this thesis is to develop such a theoretical framework for the characterisation of nonlocality as a resource. To gain a better understanding of nonlocal correlations it will be necessary to investigate correlation scenarios that go beyond the situation originally considered by Bell. In doing so, this thesis provides new description of nonlocality that also have implications for the characterisation of quantum correlations and the detection of new forms of nonlocality. The first question we address is how nonlocality can consistently be defined in a scenario of arbitrarily many parties that may collaborate among each other. To this end we recognise which are the allowed physical operations in this situation and then define nonlocality as the resource that cannot be created by these operations. Our approach shows that the conventional definition of multipartite nonlocality, adopted by the community so far, is inconsistent with this operational definition; we further propose and analyse new models that do not suffer from these inconsistencies. Furthermore, we show that our findings have implications for the characterisation of quantum correlations. A recent approach to describe the set of quantum correlation consists in using principles inspired from information theory. By using a special instance of the models we defined earlier we show a fundamental limitation of this approach: no bipartite information principle is sufficient to single out the set of quantum correlations from the set of nonsignalling correlations. We then developed a description of nonlocality in an even more generalised scenario of several parties. Motivated by a result of Popescu we study scenarios where the parties are allowed to perform not only a single but sequences of measurements on their systems. Characterising nonlocality also in this scenario in operational terms and defining local models compatible with this definition, we show that a new form of nonlocality can be detected Lastly, we examine the problem of detecting the presence of nonlocality in a multipartite scenario when one is given only partial access to the global system. We find that one can verify that the total system must display nonlocality, even though the accessible subsystems only exhibit local correlations.
Nonlocal correlations arise from measurements on tripartite entangled states can be classified into two types, one genuinely 3−way nonlocal and other local with respect to some bipartition. Still, whether a genuine tripartite entangled quantum state can exhibit genuine 3−way nonlocality, remains a challenging problem so far as measurement context is concerned. Here we introduce a novel approach in this regard. We consider three genuine tripartite mixed entangled quantum states none of which is genuinely 3−way nonlocal in original Bell scenario, but they can exhibit genuine 3−way nonlocality when distributed in some suitable multiple entanglement swapping network. So, genuine 3−way nonlocality is a nonadditive resource, which can be activated. Our result implies that genuine 3−way nonlocality of quantum states strongly depends on the measurement context contrary to the belief that genuine 3−way nonlocality can be exhibited only in original Bell scenario.
Quantum nonlocality arising from entangled particles cannot be explained by any classical notion of local causality. In the standard Bell scenario with a source and two measurement stations, entangled states can lose their ability to exhibit nonlocality due to noisy conditions. Given the fundamental and technological significance of nonlocality and the fact that these noisy entangled states can naturally arise in practical situations, it is of utmost importance to unveil their nonlocality. Here, we demonstrate that nonlocal correlations can be generated from quantum states that cannot show nonlocality in bipartite Bell scenarios. We show how to robustly characterize these states and experimentally activate their nonlocality when embedded in a photonic network, by violating classical constraints in this quantum network. These results have implications in foundations of quantum nonlocality and direct applications to quantum technologies by significantly increasing the robustness of nonlocal correlations to noise.
Quantum entanglement and nonlocality are inextricably linked. However, while entanglement is necessary for nonlocality, it is not always sufficient in the standard Bell scenario. We derive sufficient conditions for entanglement to give rise to genuine multipartite nonlocality in networks. We find that any network where the parties are connected by bipartite pure entangled states is genuine multipartite nonlocal, independently of the amount of entanglement in the shared states and of the topology of the network. As an application of this result, we also show that all pure genuine multipartite entangled states are genuine multipartite nonlocal in the sense that measurements can be found on finitely many copies of any genuine multipartite entangled state to yield a genuine multipartite nonlocal behavior. Our results pave the way toward feasible manners of generating genuine multipartite nonlocality using any connected network.
Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been separately investigated. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources allows for the certification of the non-classicality of all sources. In this paper, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high fidelity photonic quantum network by violating a single network Bell inequality.