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arXiv:2506.08128 · APS Open Science

Nonlocality in continuous-variable quantum networks

Anonymous, Amit Kundu, A. S. Majumdar

Published Aug 4, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum networks enable forms of nonlocality beyond the standard Bell scenario, with a multitude of potential applications. Continuous-variable (CV) platforms are particularly attractive for large-scale networks, offering deterministic entanglement generation and favorable prospects for long-distance distribution. Here, we present a formalism to study CV network nonlocality using pseudospin measurements. Considering the linear chain and star configurations, we derive the maximal violations of the corresponding network locality inequalities for arbitrary two-mode states. Using two-mode squeezed vacuum states, we show that the strength of nonlocality in the star configuration remains independent of the network size. Moreover, the nonlocal correlations persist even at arbitrarily high temperatures provided the squeezing exceeds a critical threshold. Further, we demonstrate non-Gaussianity as an enhancer of network nonlocality through illustrations of various classes of non-Gaussian resources. Remarkably, a coherent superposition of single-photon subtractions across modes achieves maximal violation for arbitrarily small squeezing. Finally, we provide schematics of an experimentally feasible implementation of CV network nonlocality based on the isomorphism between pseudospin and spatial parity observables.

DOI
10.1103/dklm-6g7s

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Quantum networks enable forms of nonlocality beyond the standard Bell scenario, with a multitude of potential applications. Continuous-variable (CV) platforms are particularly attractive for large-scale networks, offering deterministic entanglement generation and favorable prospects for long-distance distribution. Here, we present a formalism to study CV network nonlocality using pseudospin measurements. Considering the linear chain and star configurations, we derive the maximal violations of the corresponding network locality inequalities for arbitrary two-mode states. Using two-mode squeezed vacuum states, we show that the strength of nonlocality in the star configuration remains independent of the network size. Moreover, the nonlocal correlations persist even at arbitrarily high temperatures provided the squeezing exceeds a critical threshold. Further, we demonstrate non-Gaussianity as an enhancer of network nonlocality through illustrations of various classes of non-Gaussian resources. Remarkably, a coherent superposition of single-photon subtractions across modes achieves maximal violation for arbitrarily small squeezing. Finally, we provide schematics of an experimentally feasible implementation of CV network nonlocality based on the isomorphism between pseudospin and spatial parity observables.
The launch of a satellite capable of distributing entanglement through long distances and the first loophole-free violation of Bell inequalities are milestones indicating a clear path for the establishment of quantum networks. However, nonlocality in networks with independent entanglement sources has only been experimentally verified in simple tripartite networks, via the violation of bilocality inequalities. Here, by using a scalable photonic platform, we implement star-shaped quantum networks consisting of up to five distant nodes and four independent entanglement sources. We exploit this platform to violate the chained n-locality inequality and thus witness, in a device-independent way, the emergence of nonlocal correlations among the nodes of the implemented networks. These results open new perspectives for quantum information processing applications in the relevant regime where the observed correlations are compatible with standard local hidden variable models but are non-classical if the independence of the sources is taken into account.
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This thesis focuses on fundamental resources in quantum information theory with continuous variables and their applications to quantum optics and quantum thermodynamics. Our analysis mainly considers Gaussian states of continuous variable systems formed by two, three, or more modes, and adopts a variety of techniques to study their static and dynamical properties. Our original results include three main case studies: (i) quantifying genuine multipartite Bell nonlocality in permutationally invariant Gaussian states; (ii) characterising bipartite Einstein-Podolsky-Rosen (EPR) steering with non-Gaussian measurements; and (iii) benchmarking the reaction-coordinate mapping in non-equilibrium quantum harmonic chains. In project (i), we investigate genuine multipartite nonlocality of multimode Gaussian states, as detected by the violation of Svetlichny inequality. We consider both displaced parity and pseudospin measurements and identify the largest violation of the inequality on permutationally invariant states. In the pseudospin case, we show that the maximum violation of Svetlichny inequality allowed by quantum mechanics can be approached for asymptotically large squeezing. In project (ii) we study the detection of EPR steering (an asymmetric quantum correlation intermediate between entanglement and Bell nonlocality) in bipartite Gaussian states by pseudospin measurements. Our analysis reveals previously unexplored regimes where non-Gaussian measurements are more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. Finally, in project (iii) we analyze the validity of the reaction-coordinate mapping to characterise heat transport in an exactly solvable model: a two-node linear "quantum wire" connecting two baths at different temperatures. We find surprisingly that the stationary state of the original problem can be reproduced accurately by a weak-coupling treatment even in the regime of very strong residual dissipation.
Bell nonlocality refers to correlations between two distant, entangled particles that challenge classical notions of local causality. Beyond its foundational significance, nonlocality is crucial for device-independent technologies like quantum key distribution and randomness generation. Nonlocality quickly deteriorates in the presence of noise, and restoring nonlocal correlations requires additional resources. These often come in the form of many instances of the input state and joint measurements, incurring a significant resource overhead. Here, we experimentally demonstrate that single copies of Bell-local states, incapable of violating any standard Bell inequality, can give rise to nonlocality after being embedded into a quantum network of multiple parties. We subject the initial entangled state to a quantum channel that broadcasts part of the state to two independent receivers and certify the nonlocality in the resulting network by violating a tailored Bell-like inequality. We obtain these results without making any assumptions about the prepared states, the quantum channel, or the validity of quantum theory. Our findings have fundamental implications for nonlocality and enable the practical use of nonlocal correlations in real-world applications, even in scenarios dominated by noise.
The multipartite quantum networks feature multiple independent sources, in contrast to the conventional multipartite Bell experiment involving a single source. Despite the initial independence of resources, the multiple observers in the network can suitably choose measurements on their local subsystems and generate a form of quantum nonlocality across the network. So far, network nonlocality has been explored when each source produces a two-qubit entangled state. In this work we demonstrate the network nonlocality when each party performs a black-box measurement, and the dimension of the system remains unspecified. In an interesting work, by considering each source produces two-qubit entangled states in the conventional bilocal scenario, Gisin et al. [Phys. Rev. A 96, 020304 (2017)] demonstrated a correspondence between the violations of bipartite Clauser-Horne-Shimony-Halt inequality and the bilocality inequality. We introduce a variant of the sum-of-squares approach to reproduce their results without assuming the dimension of the system. We then generalize the argument for network nonlocality in star-network topology. Furthermore, we propose a set of nnn-locality inequalities in a star-network configuration where each of the nnn parties performs an arbitrary number of dichotomic measurements and demonstrates the above correspondence between the quantum violations of the nnn-locality inequalities and the chained Bell inequalities. A similar correspondence is demonstrated based on a recently formulated family of nnn-locality inequalities whose optimal quantum violation cannot be obtained when each source emits a two-qubit entangled state and requires multiple copies of two-qubit entangled states. Throughout this paper, each party in the network performs black-box measurements, and the dimension of the system remains unspecified.
The exploration of the concept of nonlocality beyond standard Bell scenarios in quantum network architectures unveils fundamentally new forms of correlations that hold a strong potential for future applications of quantum communication networks [1]. It is necessary to adapt theoretical advances to realistic configurations to materialize this potential. Here we consider a quantum triangle network, illustrated in Fig. 1, for which it was shown in theory that, remarkably, quantum nonlocality without inputs can be demonstrated for sources with an arbitrarily small level of independence [2]. We realize experimentally such correlated sources,ρAB,ρAC\rho_{AB}, \rho_{AC}ρAB​,ρAC​, andρBC\rho_{BC}ρBC​, by carefully engineering the output state of a single AlGaAs multiplexed entangled-photon source [3], exploiting energy-matched channels cut in its broad spectrum. This simulated triangle network is then used to violate a Bell-like inequality that we derive to capture the effect of noise in the correlations present in our system [4]. We also rigorously validate our findings by analyzing the mutual information between the generated states. Our results allow us to deepen our understanding of network nonlocality while also pushing its practical relevance for quantum communication networks.