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arXiv:1010.0900 · Nature Communications

Quantum networks reveal quantum nonlocality

Daniel Cavalcanti, Mafalda L. Almeida, Valerio Scarani, Antonio Acín

Published Feb 8, 2011• 129 citations
arXivHTMLPDF
DOI
10.1038/ncomms1193

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The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.
In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open question is to identify the minimal network configuration in which quantum resources produce Bell nonlocal correlations. Here we address this question and show that quantum nonlocality is possible in the triangle network where the parties have no input choices and produce only binary-valued outcomes. To do so, we start by identifying a family of target distributions and proving their nonlocality. Next, we construct an explicit quantum model that reproduces the target distributions to machine precision. For this, we develop an efficient method for parameterizing quantum distributions in networks, inspired by the formalism of higher-order quantum operations. When considering the number of observed variables and their cardinality, this constitutes the smallest scenario possible that supports quantum nonlocality in networks. Moreover, by analyzing the explicit quantum model, we obtain new insights into how nonlocal distributions can be generated in quantum 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.