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arXiv:2607.04656

Measurement Geometry as a Resource for Certifying Network Nonlocality

Leon Adachi, Le Bin Ho

quant-phSubmitted Jul 6, 2026• Announced Jul 7, 2026• 0 citations
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Abstract

Quantum networks can exhibit nonclassical correlations that cannot be explained by classical models with independent sources. While the role of entanglement is well understood, the impact of measurement design remains largely unexplored. Here we develop an operational framework for certifying network nonlocality in the bilocal Alice--Bob--Charlie network using ancilla-assisted meters to evaluate the nonlocal observables required for bilocal and fully network nonlocal (FNN) witnesses. The approach successfully reproduces both bilocal and FNN correlations in simulation. On the 156-qubit superconducting processor \textit{ibm\_kingston}, we observe bilocal nonlocality with $\mathcal{S}_{\rm BLHV}=1.067(6)>1$ after readout-error mitigation, while the FNN witnesses reach $99\%$ and $96\%$ of their certification thresholds, implying the substantially stronger requirements for FNN certification. We further show that Bob's joint measurement determines the accessible level of network nonlocality: bilocal and FNN certification are optimized by different measurement settings, while both violations can disappear even for maximally entangled states. These results identify measurement geometry as an independent resource for network nonlocality and provide a practical route toward its certification on programmable quantum processors.

Comments
11 pages, 9 figures

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Quantum networks can exhibit nonclassical correlations that cannot be explained by classical models with independent sources. While the role of entanglement is well understood, the impact of measurement design remains largely unexplored. Here we develop an operational framework for certifying network nonlocality in the bilocal Alice--Bob--Charlie network using ancilla-assisted meters to evaluate the nonlocal observables required for bilocal and fully network nonlocal (FNN) witnesses. The approach successfully reproduces both bilocal and FNN correlations in simulation. On the 156-qubit superconducting processor \textit{ibm_kingston}, we observe bilocal nonlocality with SBLHV=1.067(6)>1\mathcal{S}_{\rm BLHV}=1.067(6)>1SBLHV​=1.067(6)>1 after readout-error mitigation, while the FNN witnesses reach 99%99\%99% and 96%96\%96% of their certification thresholds, implying the substantially stronger requirements for FNN certification. We further show that Bob's joint measurement determines the accessible level of network nonlocality: bilocal and FNN certification are optimized by different measurement settings, while both violations can disappear even for maximally entangled states. These results identify measurement geometry as an independent resource for network nonlocality and provide a practical route toward its certification on programmable quantum processors.
Quantum correlations in networks with independent sources have revealed novel forms of nonclassical behavior. While entanglement in the sources is a necessary ingredient, the role played by entanglement in the measurements remains largely unexplored. In particular, all existing demonstrations of full network nonlocality, certifying the nonclassicality of every source in the network, have relied on entangled measurements performed at a central node with no inputs. In this work, we construct an explicit strategy that does not rely on entangled measurements, yet still achieves full network nonlocality. Our approach is based on separable measurements augmented with bidirectional classical feedforward. We further show that this same class of measurements can give rise to another recently proposed form of network nonlocality, the minimal network nonclassicality, which ensures that the observed correlations cannot be attributed to any fixed subset of nonclassical sources within the network. Finally, building on a recently developed certification framework, we quantify the amount of device-independent randomness that can be extracted from full network nonlocal correlations under different measurement strategies. Beyond their foundational significance, our results also offer a practically attractive route toward experimental implementations of network nonlocality, as they remove the need for entangled measurements.
Quantum correlation between nodes in a network which consist of several independent sources of entanglement and in multipartite entanglement systems are important for general understanding of the nature of nonlocality, quantum information processing and communication. In previous years, demonstrations of network nonlocality for bilocal scenarios have been in the focus. Yet, it has been found that the seminal protocols do not certify entanglement between end nodes, which otherwise require all sources in the network to be of nonlocal nature. This has motivated for development of even stronger concept, called full network nonlocality. Here, we experimentally demonstrate full network nonlocal correlations in a network. Specifically, we use two pairs of polarization entangled qubits created by two separate and independent entanglement sources and a partial Bell state measurement. Our results may pave the way for the use of nonlocality test in quantum communication protocols with a full network nonlocality certification.
Network Nonlocality is an advanced study of quantum nonlocality that comprises network structure beyond Bell's theorem. The development of quantum networks has the potential to bring a lot of technological applications in sevaral quantum information processing tasks. Here, we are focusing on how the role of the independence of the measurement choices of the end parties in a network works and can be used to enhance the security in a quantum network. In both three-parties two-sources bilocal network and four-parties three-sources star network scenarios, we are able to show, a practical way to understand the relaxation of the assumptions to enhance a real security protocol if someone wants to breach in a network communications. Theoratically, we have proved that by relaxing the independence of the measurement choices of only one end party we can create a Standard Network Nonlocality(SNN) and more stronger Full Network Nonlocality(FNN) and we can get maximum quantum violation by the classical no-signalling local model. We are able to distinguish between two types of network nonlocality in the sense that the FNN is stronger than SNN, i.e., FNN states all the sources in a network need to distribute nonlocal resources.
While quantum networks have been extensively studied as a natural extension of the standard Bell scenario with a richer correlation structure, general constructions of nonlinear Bell inequalities with self-testing properties are still largely lacking. In this work, we present a general method for constructing such inequalities in the simplest network scenario, in which two independent sources distribute bipartite quantum states to three spatially separated observers. These inequalities allow for arbitrary numbers of binary measurements and are maximally violated by maximally entangled states of the corresponding local dimensions together with sets of pairwise anticommuting Clifford observables. Importantly, their maximal quantum values can be determined analytically, which makes them particularly promising for device-independent applications. In particular, we prove that these Bell inequalities can be used to device-independently certify the underlying quantum network, including both the quantum states produced by the sources and the observables measured by all parties. To the best of our knowledge, this is the first self-testing result for quantum networks that relies solely on the maximal violation of a nonlocality witness.
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.
Bell's theorem shows that quantum theory is incompatible with local hidden-variable models. In recent years, research on nonlocality has moved beyond Bell's original scenario to quantum networks, where multiple independent sources distribute physical systems among distant parties, giving rise to correlations certified by nonlinear rather than standard Bell inequalities. Here, we introduce a self-guided protocol that variationally optimizes each party's measurement to maximize the violation of a network Bell inequality, with the violation evaluated efficiently at each step via local Pauli classical shadows and the search driven by the Complex Simultaneous Perturbation Stochastic Approximation (CSPSA) algorithm. Once converged, the measurement settings it returns are implemented directly and the inequality is re-evaluated without shadows. This two-stage structure separates a device-dependent search from a certificate that depends only on the observed statistics and on the causal structure of the network. We validate the protocol by numerically simulating it on the triangle network using the Wagon-Wheel inequality, recovering the violation achieved by the Fritz distribution, and extending the certification to non-maximally entangled and noisy states.