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

Physical Review A

Network nonlocality sharing in a two-forked tree-shaped network

Hao Sun, Fen-Zhuo Guo, Haifeng Dong, Fei Gao

Published Jul 1, 2024• 7 citations
Publisher

Abstract

Quantum network nonlocality sharing provides a unique perspective for constructing large-scale quantum networks and holds promise for numerous potential applications. In this paper we demonstrate the network nonlocality sharing via unsharp measurements in a two-forked $n$-layer tree-shaped network, which features ${2}^{n}\ensuremath{-}2$ independent sources and ${2}^{n}\ensuremath{-}1$ nodes. We investigate the $({2}^{n}\ensuremath{-}2)$-local scenarios via any $m$-sided sequential measurements, and conclude that arbitrarily many independent observers on each sequential side can share the non-$({2}^{n}\ensuremath{-}2)$-locality for a sufficiently large value of $n$. For a finite $n$, we present a method that enables directly obtaining the number of observers on each sequential side, who can share the non-$({2}^{n}\ensuremath{-}2)$-locality simultaneously. To interpret our results more intuitively, we discuss the simplest case of $n=3$, and find that at most 30, 6, 3, and 2 sequential observers per sequential side can simultaneously share the non-6-locality in $m$-sided cases for $m=1,2,3,4$, respectively.

DOI
10.1103/physreva.110.012401

Related papers

Network nonlocality sharing in the star-shaped scenario using only projective measurements

Hao Sun, Fen-Zhuo Guo, Haifeng Dong +2 more

Sequential measurements present a novel framework for constructing large-scale quantum networks, particularly in quantum correlation sharing. In this paper, we design projective measurements and combination strategies to achieve nonlocality sharing in star-shaped networks by leveraging shared classical randomness. This network consists of $n$ branches, each containing one or two sequential observers. By investigating two-sided nonlocality sharing within a 2-local network, we identify the optimal projective measurement combination strategy based on the double violation of the 2-locality inequality. Utilizing this optimal strategy, we demonstrate that four inequalities can be violated simultaneously in the 2-local scenario. Furthermore, in an $n$-local scenario involving $m$ ($1\ensuremath{\le}m\ensuremath{\le}n$) branches with two sequential observers, our optimal strategy shows that non-$n$-locality sharing among all observers can be achieved through the simultaneous violation of ${2}^{m} n$-locality inequality. Our findings provide a distinctive perspective on quantum correlation sharing in networks.

Physical Review A•Feb 3, 2025•4 citations

Sharing nonlocality in a quantum network by unbounded sequential observers

Shyam Sundar Mahato, A. K. Pan

Of late, there has been an upsurge of interest in studying the sequential sharing of various forms of quantum correlations, viz., nonlocality, preparation contextuality, coherence, and entanglement. In this work, we explore the sequential sharing of nonlocality in a quantum network. We first consider the simplest case of the two-input bilocality scenario that features two independent sources and three parties, including two edge parties and a central party. We demonstrate that, in the symmetric case when the sharing is considered for both the edge parties, the nonlocality can be shared by, at most, two sequential observers per edge party. However, in the asymmetric case, when the sharing across one edge party is considered, we show that, at most, six sequential observers can share the nonlocality in the network. We extend our investigation to the two-input $n$-local scenario in the star-network configuration that features an arbitrary $n$ number of edge parties and one central party. In the asymmetric case, we demonstrate that the network nonlocality can be shared by an unbounded number of sequential observers across one edge party for a suitably large value of $n$. Further, we generalize our study for an arbitrary $m$ input $n$-local scenario in the star-network configuration. We show that, even for an arbitrary $m$ input scenario, the nonlocality can be shared by an unbounded number of sequential observers. However, increasing the input $m$, one has to employ a larger number of edge parties $n$ than that of the two-input case to demonstrate the sharing of an unbounded number of sequential observers.

arXiv:2212.14325•Physical Review A•Oct 24, 2022•19 citations

Quantum Nonlocality in Any Forked Tree-Shaped Network

Li‐Hua Yang, Xiaofei Qi, Jinchuan Hou

In the last decade, much attention has been focused on examining the nonlocality of various quantum networks, which are fundamental for long-distance quantum communications. In this paper, we consider the nonlocality of any forked tree-shaped network, where each node, respectively, shares arbitrary number of bipartite sources with other nodes in the next "layer". The Bell-type inequalities for such quantum networks are obtained, which are, respectively, satisfied by all (tn-1)-local correlations and all local correlations, where tn denotes the total number of nodes in the network. The maximal quantum violations of these inequalities and the robustness to noise in these networks are also discussed. Our network can be seen as a generalization of some known quantum networks.

Entropy•May 13, 2022•16 citations

Persistency of quantum non-multi-local correlations in noisy acyclic networks

Shuyuan Yang, Jinchuan Hou, Kan He

Abstract The topic of network quantum nonlocal correlations arises from the large-scale quantum communications. It has been demonstrated that non-m-local correlations (m is the number of sources) in some special kinds of networks will decay under the influence of noises from imperfect devices as these networks extend, including linear and star networks. Furthermore, we observe that under the same noisy level, persistency of non-multi-local correlations in aforementioned different kinds of networks appears obvious discrepancy. Therefore, it becomes a natural and challenging task to check the persistency of non-multi-locality in more complex acyclic network, since star and linear networks can be regarded as acyclic networks. It is worth noting that an acyclic network is one indeterminate forked tree-shaped networks. So the study is focused on the tree-shaped network. We first devote to discussing the determinate forked case. We obtain inequality persistency criteria of determinate k-forked tree-shaped network non-(s n (k))-local correlations (s n (k) is the number of total sources). We show that the larger the fork number k is larger, the better the non-multi-locality of this network persists. In the indeterminate forked case, the inequality persistency criteria are also established. We observe that the larger the number of parties in the last layer of an acyclic network, the better the non-multi-locality of this network is persisted. This theoretical research may guide us how to build quantum networks with the stronger correlation in practical communications.

Physica Scripta•Mar 20, 2024•1 citation

Limits of network nonlocality probed by timelike-separated observers

Pritam Halder, Ratul Banerjee, Shiladitya Mal +1 more

In an entanglement swapping scenario, if two sources distributing entangled states between three parties are independent, local correlations lead to a different kind of inequality than the standard Bell inequalities, known as network local models. A highly demanding task is to find out a way to involve many players nontrivially in a quantum network since measurements, in general, disturb the system. To this end, we consider here an alternative way of sharing network nonlocality when two observers initially share a maximally entangled, a nonmaximally entangled and a noisy entangled state. We report that by employing unsharp measurements performed by one of the observers, at most six pairs can sequentially demonstrate the violation of bilocal inequality while a maximum of two pairs of observers can exhibit bi-nonlocality when both the observers perform unsharp measurements. We also find the critical noise involved in unsharp measurements in each round to illustrate the bi-nonlocality for a fixed shared entangled state as a resource. We also connect the entanglement content of the shared state, quantified via von-Neumann entropy for pure states and entanglement of formation for Werner states with the maximum number of rounds showing violation of bilocal inequality. By considering elegant joint measurement at the node such that the entanglement content in the elements of the joint measurement by the third party gets reduced, we observe that the maximum number reduces to two sequential sharing of bi-nonlocality even for the maximally entangled state when the settings at each side are taken to be three and fixed.

arXiv:2203.05353•Physical Review A•Nov 14, 2022•6 citations

Quantum steering in two-forked tree-shaped networks

Shuyuan Yang, Kan He, Xiaofei Qi +1 more

Abstract Network quantum steering (NQS) arises from network models required with classification of trusted and untrusted parties. The network local hidden state (NLHS) models have first been proposed to define the NQS in a linear network with end points being trusted. In the paper, we devote to establishing the NLHS model to define the NQS in a kind of more complex and applied-extensively networks, namely, the two-forked tree-shaped network. Here we assume that the parties at the last layer are trusted while the remaining parties are untrusted in this network. According to the NLHS model, we observe that network nonlocality implies network steerability. Furthermore, we pay more attentions to discovering the relationship between the network quantum unsteerability and separability/unsteerability of bipartite sources in this two-forked tree-shaped network. Moreover, we generalize two kinds of bipartite steering inequality criteria as the NQS criteria. They are built based on statistical quantities, which can be directly evaluated in experiments.

Physica Scripta•Oct 18, 2023•4 citations
Quantum network nonlocality sharing provides a unique perspective for constructing large-scale quantum networks and holds promise for numerous potential applications. In this paper we demonstrate the network nonlocality sharing via unsharp measurements in a two-forked nnn-layer tree-shaped network, which features 2n\ensuremath−2{2}^{n}\ensuremath{-}22n\ensuremath−2 independent sources and 2n\ensuremath−1{2}^{n}\ensuremath{-}12n\ensuremath−1 nodes. We investigate the (2n\ensuremath−2)({2}^{n}\ensuremath{-}2)(2n\ensuremath−2)-local scenarios via any mmm-sided sequential measurements, and conclude that arbitrarily many independent observers on each sequential side can share the non-(2n\ensuremath−2)({2}^{n}\ensuremath{-}2)(2n\ensuremath−2)-locality for a sufficiently large value of nnn. For a finite nnn, we present a method that enables directly obtaining the number of observers on each sequential side, who can share the non-(2n\ensuremath−2)({2}^{n}\ensuremath{-}2)(2n\ensuremath−2)-locality simultaneously. To interpret our results more intuitively, we discuss the simplest case of n=3n=3n=3, and find that at most 30, 6, 3, and 2 sequential observers per sequential side can simultaneously share the non-6-locality in mmm-sided cases for m=1,2,3,4m=1,2,3,4m=1,2,3,4, respectively.
Sequential measurements present a novel framework for constructing large-scale quantum networks, particularly in quantum correlation sharing. In this paper, we design projective measurements and combination strategies to achieve nonlocality sharing in star-shaped networks by leveraging shared classical randomness. This network consists of nnn branches, each containing one or two sequential observers. By investigating two-sided nonlocality sharing within a 2-local network, we identify the optimal projective measurement combination strategy based on the double violation of the 2-locality inequality. Utilizing this optimal strategy, we demonstrate that four inequalities can be violated simultaneously in the 2-local scenario. Furthermore, in an nnn-local scenario involving mmm ($1\ensuremath{\le}m\ensuremath{\le}n$) branches with two sequential observers, our optimal strategy shows that non-nnn-locality sharing among all observers can be achieved through the simultaneous violation of 2mn{2}^{m} n2mn-locality inequality. Our findings provide a distinctive perspective on quantum correlation sharing in networks.
Of late, there has been an upsurge of interest in studying the sequential sharing of various forms of quantum correlations, viz., nonlocality, preparation contextuality, coherence, and entanglement. In this work, we explore the sequential sharing of nonlocality in a quantum network. We first consider the simplest case of the two-input bilocality scenario that features two independent sources and three parties, including two edge parties and a central party. We demonstrate that, in the symmetric case when the sharing is considered for both the edge parties, the nonlocality can be shared by, at most, two sequential observers per edge party. However, in the asymmetric case, when the sharing across one edge party is considered, we show that, at most, six sequential observers can share the nonlocality in the network. We extend our investigation to the two-input nnn-local scenario in the star-network configuration that features an arbitrary nnn number of edge parties and one central party. In the asymmetric case, we demonstrate that the network nonlocality can be shared by an unbounded number of sequential observers across one edge party for a suitably large value of nnn. Further, we generalize our study for an arbitrary mmm input nnn-local scenario in the star-network configuration. We show that, even for an arbitrary mmm input scenario, the nonlocality can be shared by an unbounded number of sequential observers. However, increasing the input mmm, one has to employ a larger number of edge parties nnn than that of the two-input case to demonstrate the sharing of an unbounded number of sequential observers.
In the last decade, much attention has been focused on examining the nonlocality of various quantum networks, which are fundamental for long-distance quantum communications. In this paper, we consider the nonlocality of any forked tree-shaped network, where each node, respectively, shares arbitrary number of bipartite sources with other nodes in the next "layer". The Bell-type inequalities for such quantum networks are obtained, which are, respectively, satisfied by all (tn-1)-local correlations and all local correlations, where tn denotes the total number of nodes in the network. The maximal quantum violations of these inequalities and the robustness to noise in these networks are also discussed. Our network can be seen as a generalization of some known quantum networks.
Abstract The topic of network quantum nonlocal correlations arises from the large-scale quantum communications. It has been demonstrated that non-m-local correlations (m is the number of sources) in some special kinds of networks will decay under the influence of noises from imperfect devices as these networks extend, including linear and star networks. Furthermore, we observe that under the same noisy level, persistency of non-multi-local correlations in aforementioned different kinds of networks appears obvious discrepancy. Therefore, it becomes a natural and challenging task to check the persistency of non-multi-locality in more complex acyclic network, since star and linear networks can be regarded as acyclic networks. It is worth noting that an acyclic network is one indeterminate forked tree-shaped networks. So the study is focused on the tree-shaped network. We first devote to discussing the determinate forked case. We obtain inequality persistency criteria of determinate k-forked tree-shaped network non-(s n (k))-local correlations (s n (k) is the number of total sources). We show that the larger the fork number k is larger, the better the non-multi-locality of this network persists. In the indeterminate forked case, the inequality persistency criteria are also established. We observe that the larger the number of parties in the last layer of an acyclic network, the better the non-multi-locality of this network is persisted. This theoretical research may guide us how to build quantum networks with the stronger correlation in practical communications.
In an entanglement swapping scenario, if two sources distributing entangled states between three parties are independent, local correlations lead to a different kind of inequality than the standard Bell inequalities, known as network local models. A highly demanding task is to find out a way to involve many players nontrivially in a quantum network since measurements, in general, disturb the system. To this end, we consider here an alternative way of sharing network nonlocality when two observers initially share a maximally entangled, a nonmaximally entangled and a noisy entangled state. We report that by employing unsharp measurements performed by one of the observers, at most six pairs can sequentially demonstrate the violation of bilocal inequality while a maximum of two pairs of observers can exhibit bi-nonlocality when both the observers perform unsharp measurements. We also find the critical noise involved in unsharp measurements in each round to illustrate the bi-nonlocality for a fixed shared entangled state as a resource. We also connect the entanglement content of the shared state, quantified via von-Neumann entropy for pure states and entanglement of formation for Werner states with the maximum number of rounds showing violation of bilocal inequality. By considering elegant joint measurement at the node such that the entanglement content in the elements of the joint measurement by the third party gets reduced, we observe that the maximum number reduces to two sequential sharing of bi-nonlocality even for the maximally entangled state when the settings at each side are taken to be three and fixed.
Abstract Network quantum steering (NQS) arises from network models required with classification of trusted and untrusted parties. The network local hidden state (NLHS) models have first been proposed to define the NQS in a linear network with end points being trusted. In the paper, we devote to establishing the NLHS model to define the NQS in a kind of more complex and applied-extensively networks, namely, the two-forked tree-shaped network. Here we assume that the parties at the last layer are trusted while the remaining parties are untrusted in this network. According to the NLHS model, we observe that network nonlocality implies network steerability. Furthermore, we pay more attentions to discovering the relationship between the network quantum unsteerability and separability/unsteerability of bipartite sources in this two-forked tree-shaped network. Moreover, we generalize two kinds of bipartite steering inequality criteria as the NQS criteria. They are built based on statistical quantities, which can be directly evaluated in experiments.