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arXiv:2401.15428 · Physical Review Letters

Experimental Genuine Quantum Nonlocality in the Triangle Network

Ningning Wang, Chao Zhang, Huan Cao, Kai Xu, Bi‐Heng Liu, Yun‐Feng Huang, Chuan-Feng Li, Guang-Can Guo, N. Gisin, Tamás Kriváchy, Marc-Olivier Renou

Published Apr 3, 2026• 1 citation
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Abstract

In the last decade, it was understood that quantum networks involving several independent sources of entanglement which are distributed and measured by several parties allowed for completely novel forms of nonclassical quantum correlations, when entangled measurements are performed. Here, we experimentally obtain quantum correlations in a triangle network structure and provide solid evidence of its nonlocality. Specifically, we first obtain the Elegant distribution proposed in [Gisin et al., Entanglement 25 years after quantum teleportation: Testing joint measurements in quantum networks, Entropy 21, 325 (2019)ENTRFG1099-430010.3390/e21030325] by performing a six-photon experiment. Then, we justify its nonlocality based on machine learning tools to estimate the distance of the experimentally obtained correlation to the local set.

DOI
10.1103/5hhc-rw3t

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In the last decade, it was understood that quantum networks involving several independent sources of entanglement which are distributed and measured by several parties allowed for completely novel forms of nonclassical quantum correlations, when entangled measurements are performed. Here, we experimentally obtain quantum correlations in a triangle network structure and provide solid evidence of its nonlocality. Specifically, we first obtain the Elegant distribution proposed in [Gisin et al., Entanglement 25 years after quantum teleportation: Testing joint measurements in quantum networks, Entropy 21, 325 (2019)ENTRFG1099-430010.3390/e21030325] by performing a six-photon experiment. Then, we justify its nonlocality based on machine learning tools to estimate the distance of the experimentally obtained correlation to the local set.
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Quantum networks allow in principle for completely novel forms of quantum correlations. In particular, quantum nonlocality can be demonstrated here without the need of having various input settings, but only by considering the joint statistics of fixed local measurement outputs. However, previous examples of this intriguing phenomenon all appear to stem directly from the usual form of quantum nonlocality, namely via the violation of a standard Bell inequality. Here we present novel examples of "quantum nonlocality without inputs," which we believe represent a new form of quantum nonlocality, genuine to networks. Our simplest examples, for the triangle network, involve both entangled states and joint entangled measurements. A generalization to any odd-cycle network is also presented.
Abstract Defining nonlocality in a no‐input closed quantum network scenario is a new area of interest nowadays. Gisin, in [Entropy 21, 325 (2019)], proposed a possible condition for non‐tri‐locality of the trivial no‐input closed network scenario, triangle network, by introducing a new kind of joint measurement bases and a probability bound. In [npj Quantum Information (2020) 6:70] they found a shred of numerical evidence in support of Gisin's probability bound. Now based on that probability bound, it finds the nature of the correlation in a triangle network scenario. This study observes how far the probability lies from that Gisin's bound with every possible combination of entangled and local pure states distributed from three independent quantum sources. Here, it uses the generalized Elegant Joint Measurements bases for each party and find that there is a dependency of non‐locality on the entanglement of these joint measurement bases. It also checks the probability bound for the polygon structure.
Quantum networks are the center of many of the recent advances in quantum science, not only leading to the discovery of new properties in the foundations of quantum theory but also allowing for novel communication and cryptography protocols. It is known that networks beyond that in the paradigmatic Bell's theorem imply new and sometimes stronger forms of nonclassicality. Due to a number of practical difficulties, however, the experimental implementation of such networks remains far less explored. Going beyond what has been previously tested, here we verify the nonlocality of an experimental triangle network, consisting of three independent sources of bipartite entangled photon states interconnecting three distant parties. By performing separable measurements only and evaluating parallel chained Bell inequalities, we show that such networks can lead to a genuine form of tripartite nonlocality, where classical models are unable to mimic the quantum predictions even if some of the parties are allowed to communicate.
Correlations in quantum networks with independent sources exhibit a completely novel form of nonclassicality in the sense that the nonlocality of such correlations can be demonstrated in fixed local input scenarios. Before the pioneering work of Renou et al. [Phys. Rev. Lett. 123, 140401 (2019)], the nonlocal feature of such network correlations was directly attributable to standard Bell nonlocality. In the above-mentioned reference, the authors provided some of the first examples of triangle network correlations, whose nonlocality cannot be deduced from Bell-CHSH nonlocality. To date, a complete characterization of such scenarios has yet to be provided. The present work characterizes correlations arising due to fixed local measurements in a triangle network under a source independence assumption. Precisely speaking, a set of criteria is framed in the form of Bell-type inequalities, each of which is necessarily satisfied by trilocal correlations. Possible quantum violation of at least one criterion from the set is analyzed, which in turn points out the utility of the set of criteria to detect nonlocality (nontrilocality) in quantum triangle networks. Interestingly, measurement on a local product state basis turns out to be sufficient to generate nontrilocal correlations in some quantum networks. Noise tolerance of the detection criteria is discussed followed by a generalization of the framework for demonstrating correlations in any nnn-sided polygon where nnn is finite.
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.