Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1702.08316 · New Journal of Physics

Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

Francesco Andreoli, Gonzalo Carvacho, Luca Santodonato, Rafael Chaves, Fabio Sciarrino

Published Nov 14, 2017• 83 citations
arXivHTMLPDF

Abstract

Bell's theorem was a cornerstone for our understanding of quantum theory and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been attracting growing attention, but a deep characterization of quantum behavior is still missing for this novel context. In this work we analyze quantum correlations arising in the bilocality scenario, that is a tripartite quantum network where the correlations between the parties are mediated by two independent sources of states. First, we prove that non-bilocal correlations witnessed through a Bell-state measurement in the central node of the network form a subset of those obtainable by means of a local projective measurement. This leads us to derive the maximal violation of the bilocality inequality that can be achieved by arbitrary two-qubit quantum states and arbitrary local projective measurements. We then analyze in details the relation between the violation of the bilocality inequality and the CHSH inequality. Finally, we show how our method can be extended to the n -locality scenario consisting of n two-qubit quantum states distributed among n + 1 nodes of a star-shaped network.

DOI
10.1088/1367-2630/aa8b9b

Related papers

Maximal qubit violation of n -local inequalities in a quantum network

Amit Kundu, Mostak Kamal Molla, Indrani Chattopadhyay +1 more

Source-independent quantum networks are considered as a natural generalization to the Bell scenario where we investigate the nonlocal properties of quantum states distributed and measured in a network. Considering the simplest network of entanglement swapping, recently Gisin et al. [Phys. Rev. A 96, 020304(R) (2017)] and Andreoli [New. J. Phys. 19, 113020 (2017)] independently provided a systematic characterization of the set of quantum states leading to violation of the so-called bilocality inequality. In this work, we consider the complexities in quantum networks with an arbitrary number of parties distributed in chain-shaped and star-shaped networks. We derive the maximal violation of the ``$n$-local'' inequality that can be achieved by arbitrary two-qubit states for such chain- and star-shaped networks. This would further provide a deeper understanding of quantum correlations in complex structures.

arXiv:2011.03513•Physical Review A•Nov 24, 2020•35 citations

Nonlocal correlations in the star-network configuration

Armin Tavakoli, Paul Skrzypczyk, Daniel Cavalcanti +1 more

The concept of bilocality was introduced to study the correlations which arise in an entanglement-swapping scenario, where one has two sources which can naturally be taken to be independent. This additional constraint leads to stricter requirements than simply imposing locality, in the form of bilocality inequalities. In this work we consider a natural generalization of the bilocality scenario; namely, the star network consisting of a single central party surrounded by $n$ edge parties, each of which shares an independent source with the center. We derive inequalities which are satisfied by all local correlations in this scenario, for the cases when the central party performs (i) two dichotomic measurements (ii) a single Bell-state measurement. We demonstrate quantum violations of these inequalities and study both the robustness to noise and to losses.

arXiv:1409.5702•Physical Review A•Dec 4, 2014•148 citations

Device-independent certification of tripartite quantum networks with bilocal Bell inequalities

Patryk Michalski, Arturo Konderak, Remigiusz Augusiak

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.

quant-pharXiv:2607.09933•Jul 14, 2026•0 citations

Experimental violation of n-locality in a star quantum network

Davide Poderini, Iris Agresti, Guglielmo Marchese +9 more

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.

Nature Communications•May 18, 2020•60 citations

Characterizing nonlocal correlations through various n -locality inequalities in a quantum network

Sneha Munshi, A. K. Pan

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 $n$-locality inequalities in a star-network configuration where each of the $n$ parties performs an arbitrary number of dichotomic measurements and demonstrates the above correspondence between the quantum violations of the $n$-locality inequalities and the chained Bell inequalities. A similar correspondence is demonstrated based on a recently formulated family of $n$-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.

arXiv:2112.15451•Physical Review A•Mar 30, 2022•23 citations

Experimental violation of local causality in a quantum network

Gonzalo Carvacho, Francesco Andreoli, Luca Santodonato +3 more

Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols.

arXiv:1610.03327•Nature Communications•Mar 16, 2017•81 citations
Bell's theorem was a cornerstone for our understanding of quantum theory and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been attracting growing attention, but a deep characterization of quantum behavior is still missing for this novel context. In this work we analyze quantum correlations arising in the bilocality scenario, that is a tripartite quantum network where the correlations between the parties are mediated by two independent sources of states. First, we prove that non-bilocal correlations witnessed through a Bell-state measurement in the central node of the network form a subset of those obtainable by means of a local projective measurement. This leads us to derive the maximal violation of the bilocality inequality that can be achieved by arbitrary two-qubit quantum states and arbitrary local projective measurements. We then analyze in details the relation between the violation of the bilocality inequality and the CHSH inequality. Finally, we show how our method can be extended to the n -locality scenario consisting of n two-qubit quantum states distributed among n + 1 nodes of a star-shaped network.
Source-independent quantum networks are considered as a natural generalization to the Bell scenario where we investigate the nonlocal properties of quantum states distributed and measured in a network. Considering the simplest network of entanglement swapping, recently Gisin et al. [Phys. Rev. A 96, 020304(R) (2017)] and Andreoli [New. J. Phys. 19, 113020 (2017)] independently provided a systematic characterization of the set of quantum states leading to violation of the so-called bilocality inequality. In this work, we consider the complexities in quantum networks with an arbitrary number of parties distributed in chain-shaped and star-shaped networks. We derive the maximal violation of the ``nnn-local'' inequality that can be achieved by arbitrary two-qubit states for such chain- and star-shaped networks. This would further provide a deeper understanding of quantum correlations in complex structures.
The concept of bilocality was introduced to study the correlations which arise in an entanglement-swapping scenario, where one has two sources which can naturally be taken to be independent. This additional constraint leads to stricter requirements than simply imposing locality, in the form of bilocality inequalities. In this work we consider a natural generalization of the bilocality scenario; namely, the star network consisting of a single central party surrounded by nnn edge parties, each of which shares an independent source with the center. We derive inequalities which are satisfied by all local correlations in this scenario, for the cases when the central party performs (i) two dichotomic measurements (ii) a single Bell-state measurement. We demonstrate quantum violations of these inequalities and study both the robustness to noise and to losses.
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.
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.
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.
Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols.