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arXiv:1808.06336 · Physical Review A

Nonsignaling causal hierarchy of general multisource networks

Ming‐Xing Luo

Published Jun 9, 2020• 14 citations
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Abstract

Large-scale multisource networks have been employed to overcome the practical constraints that entangled systems are difficult to faithfully transmit over large distances or store over long times. However, a full characterization of the multipartite nonlocality of these networks remains out of reach, mainly due to the complexity of multipartite causal models. In this paper, we propose a general framework of Bayesian networks to reveal connections among different causal structures. The present model implies a special star-convex set of nonsignaling correlations from multisource networks that allows the construction of a polynomial-time algorithm for solving the compatibility problem of a given correlation distribution and a fixed causal network. It is then used to classify the nonlocality originating from the standard entanglement swapping of tripartite networks. Our model provides a unified device-independent information processing method for exploring the practical security against nonsignaling eavesdroppers in multisource quantum networks.

DOI
10.1103/physreva.101.062317

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Large-scale multisource networks have been employed to overcome the practical constraints that entangled systems are difficult to faithfully transmit over large distances or store over long times. However, a full characterization of the multipartite nonlocality of these networks remains out of reach, mainly due to the complexity of multipartite causal models. In this paper, we propose a general framework of Bayesian networks to reveal connections among different causal structures. The present model implies a special star-convex set of nonsignaling correlations from multisource networks that allows the construction of a polynomial-time algorithm for solving the compatibility problem of a given correlation distribution and a fixed causal network. It is then used to classify the nonlocality originating from the standard entanglement swapping of tripartite networks. Our model provides a unified device-independent information processing method for exploring the practical security against nonsignaling eavesdroppers in multisource quantum 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.
The violation of certain Bell inequalities allows for device-independent information processing secure against nonsignaling eavesdroppers. However, this only holds for the Bell network, in which two or more agents perform local measurements on a single shared source of entanglement. To overcome the practical constraints that entangled systems can only be transmitted over relatively short distances, large-scale multisource networks have been employed. Do there exist analogs of Bell inequalities for such networks, whose violation is a resource for device independence? In this Letter, the violation of recently derived polynomial Bell inequalities will be shown to allow for device independence on multisource networks, secure against nonsignaling eavesdroppers.
The Bell inequality can provide a useful witness for device-independent applications with quantum (or postquantum) eavesdroppers. This feature holds only for single entangled systems. Our goal is to explore a device-independent model for quantum networks. We first propose a Bell inequality to verify the genuinely multipartite nonlocality of connected quantum networks including cyclic networks and universal quantum computational resources for a measurement-based computation model. This is further used to construct a monogamy relation in a fully device-independent model with multisource quantum resources. It is finally applied for multiparty quantum key distribution, blind quantum computation, and quantum secret sharing. The present model can inspire various large-scale applications on quantum networks in a device-independent manner.
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.
We present a method that allows the study of classical and quantum correlations in networks with causally independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a form compatible with semidefinite programing, it enables the use of the Navascués-Pironio-Acín hierarchy in complex quantum networks. We first show how the technique successfully identifies correlations not attainable in the entanglement-swapping scenario. Then we use it to show how the nonlocal power of measurements can be activated in a network: there exist measuring devices that, despite being unable to generate nonlocal correlations in the standard Bell scenario, provide a classical-quantum separation in an entanglement swapping configuration.
The quantum network correlations play significant roles in long distance quantum communication, quantum cryptography and distributed quantum computing. Generally it is very difficult to characterize the multipartite quantum network correlations such as nonlocality, entanglement and steering. In this paper, we propose the network and the genuine network quantum steering models from the aspect of probabilities in the star network configurations. Linear and nonlinear inequalities are derived to detect the network and genuine network quantum steering when the central party performs one fixed measurement. We show that our criteria can detect more quantum network steering than that from the violation of the nnn-locality quantum networks. Moreover, it is shown that biseparable assemblages can demonstrate genuine network steering in the star network configurations.