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Laser Physics

Genuine quantum nonlocality in the quadrangle network

Yu Fan, Qing Yang, Arif Ullah, Zhi Lin, Ming Yang

Published May 7, 2026• 0 citations
Publisher

Abstract

Abstract Given the inherent complexity of network scenarios, quantum nonlocality in networks has gained renewed significance, motivating research into the subsequent fundamental challenges. Specially, networks with independent quantum sources enable the demonstration of quantum nonlocality in networks without measurement inputs–characterized by all parties performing fixed joint measurements. Here, we propose a quadrangle network scenario without inputs and demonstrate quantum nonlocality genuine to it. It is by a logical contradiction rather than the violation of some Bell-type inequality that this kind of quadrangle network nonlocality is identified, so it can not be traced back to the standard Bell nonlocality. The detailed conditions for identifying the genuine quantum nonlocality in the quadrangle network are presented in terms of the measurement entanglement and the channel entanglement, which indicates that the precise compatibility between the measurement entanglement and the channel entanglement is essential for demonstrating the quantum nonlocality genuine to the quadrangle network.

DOI
10.1088/1555-6611/ae6313

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Abstract Given the inherent complexity of network scenarios, quantum nonlocality in networks has gained renewed significance, motivating research into the subsequent fundamental challenges. Specially, networks with independent quantum sources enable the demonstration of quantum nonlocality in networks without measurement inputs–characterized by all parties performing fixed joint measurements. Here, we propose a quadrangle network scenario without inputs and demonstrate quantum nonlocality genuine to it. It is by a logical contradiction rather than the violation of some Bell-type inequality that this kind of quadrangle network nonlocality is identified, so it can not be traced back to the standard Bell nonlocality. The detailed conditions for identifying the genuine quantum nonlocality in the quadrangle network are presented in terms of the measurement entanglement and the channel entanglement, which indicates that the precise compatibility between the measurement entanglement and the channel entanglement is essential for demonstrating the quantum nonlocality genuine to the quadrangle network.
Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.
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.
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.
Nonlocality arising in networks composed of several independent sources gives rise to phenomena radically different from that in standard Bell scenarios. Over the years, the phenomenon of network nonlocality in the entanglement-swapping scenario has been well investigated and demonstrated. However, it is known that violations of the so-called bilocality inequality used in previous experimental demonstrations cannot be used to certify the nonclassicality of their sources. This has put forward a stronger concept for nonlocality in networks, called full network nonlocality. Here, we experimentally observe full network nonlocal correlations in a network where the source-independence, locality, and measurement-independence loopholes are closed. This is ensured by employing two independent sources, rapid setting generation, and spacelike separations of relevant events. Our experiment violates known inequalities characterizing nonfull network nonlocal correlations by over 5 standard deviations, certifying the absence of classical sources in the realization.
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.
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.