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arXiv:2604.11910 · Physical Review Research

Network Nonlocality with Separable Measurements

Emanuele Polino, Davide Poderini, Giorgio Minati, Giovanni Rodari, Rafael Chaves, Fabio Sciarrino

quant-phSubmitted Apr 13, 2026• Announced Apr 15, 2026• 0 citations
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Abstract

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.

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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.
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 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.
Quantum nonlocality can be demonstrated without inputs (i.e., each party using a fixed measurement setting) in a network with independent sources. Here we consider this effect on ring networks, and show that the underlying quantum strategy can be partially characterized, or self-tested, from observed correlations. Applying these results to the triangle network allows us to show that the nonlocal distribution of Renou et al. [Phys. Rev. Lett. 123, 140401 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.140401] requires that (i) all sources produce a minimal amount of entanglement, (ii) all local measurements are entangled, and (iii) each local outcome features a minimal entropy. Hence we show that the triangle network allows for genuine network quantum nonlocality and certifiable randomness.
With the increased availability of quantum technological devices, it becomes more important to have tools to guarantee their correct nonclassical behavior. This is especially important for quantum networks, which constitute the platforms where multipartite cryptographic protocols will be implemented, and where guarantees of nonclassicality translate into security proofs. We derive linear and nonlinear Bell-like inequalities for networks, whose violation certifies the absence of a minimum number of classical sources in them. We do so, first, without assuming that nature is ultimately governed by quantum mechanics, providing a hierarchy interpolating between network nonlocality and full network nonlocality. Second we insert this assumption, which leads to results more amenable to certification in experiments.
Entanglement and nonlocality are two important nonclassical features of quantum correlations. Recently the study of quantum correlations in networks has undergone remarkable progress owing to technological development towards scalable quantum networks. However, compared to the standard Bell scenario, manifestation of the interplay between these two aspects has received less attention in network scenarios featuring independent sources. In this work we have analyzed the relation between entanglement content of the sources and detectable non-nnn-locality in two distinct network topologies (linear and star). We have studied the extremal violations of nnn-local inequalities (compatible with linear and star network) for any fixed amount of entanglement (in terms of concurrence) of the independent sources. It is observed that each of the sources must be entangled for detecting non-nnn-locality in a linear network. However, the same is not true for star nnn-local network. The present analysis reveals that entanglement of all the independent sources is not a necessity for generation of non-nnn-local correlations in star topology. Characterization of sources in terms of the minimum entanglement requirement for any fixed violation amount of the nnn-local inequalities is also provided. Interestingly, detection of non-nnn-locality is ensured in the network if product of concurrence of all the sources involved exceeds 12.\frac{1}{2}.21​.
The nonlocality arising in a multiparty network involving multiple independent sources radically differs from the standard multipartite Bell nonlocality involving a single source. The notion of the full network nonlocality (FNN) [A. Pozas-Kerstjens et al., Full network nonlocality, Phys. Rev. Lett. 128, 010403 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.010403] characterizes the quantum correlations that cannot be reproduced by a local-nonlocal model featuring one local source and the rest of nonlocal no-signaling sources. However, the demonstration of FNN was limited to bilocal and trilocal star-shaped network scenarios involving three or two dichotomic measurements for edge parties. In this Letter, we first demonstrate that a large class of prevailing network inequalities does not exhibit FNN. We then introduce an elegant set of arbitrary-party and unbounded-input network inequalities in star-shaped and linear-chain networks whose optimal quantum violation exhibits FNN, certifying that the nonlocality is genuinely distributed to the entire network. Contrasting to existing demonstrations of FNN that inevitably require fixed-input and four-output elegant joint measurements for the central party, our generalized inequalities are more experimentally friendly, requiring only two output measurements. Moreover, our derivation of optimal quantum violation is fully analytic and devoid of assuming the dimension of the quantum system, thereby showcasing its potential for device-independent self-testing.