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.
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.
The process of entanglement swapping showed that suitable measurements can generate nonlocal correlations even from particles that never interacted directly. This fact was generalized to the concept of bilocality for a quantum network, where there are three observers sharing two independent sources. Since then, the nonlocality nature was explored in various quantum networks. In this work, we consider the nonlocality of $({2}^{n}\ensuremath{-}1)$-partite tree-tensor networks, which are widely used in quantum communications. We derive the Bell-type inequalities which are respectively satisfied by all $({2}^{n}\ensuremath{-}2)$-local correlations and all local correlations, and demonstrate the maximal quantum violations of these inequalities and the robustness to noise in these tree 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.
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.
Abstract The correlations in quantum networks have attracted strong interest due to the fact that linear Bell inequalities derived from one source are useless for characterizing multipartite correlations of general quantum networks. In this paper, a type of multi-star-shaped quantum networks are introduced and discussed. Such a network consists of three-grade nodes: the first grade is named party (node) A , the second one consists of m nodes marked B 1 , B 2 , …, B m , which are stars of A and the third one consists of m 2 nodes C k j ( j , k = 1 , 2 , … , m ) , where C k j ( k = 1 , 2 , … , m ) are stars of B j . We call such a network a three-grade m -star quantum network and denoted by SQN (3, m ), being as a natural extension of bilocal networks and star-shaped networks. We introduce and discussed the locality and strong locality of a SQN (3, m ) and derive the related nonlinear Bell inequalities, called (3, m )-locality inequalities and (3, m )-strong locality inequalities. To compare with the bipartite locality of quantum states, we define the separability of SQN (3, m ) that imply the locality and then locality of SQN (3, m ). When all of the shared states of the network are pure ones, we prove that SQN (3, m ) is nonlocal if and only if it is entangled.
Quantum nonlocality in networks featuring multiple independent sources underpins large-scale quantum communication and poses fundamental challenges for its characterization. In this work, we construct a family of explicit nonlinear Bell inequalities to verify the nonlocality across the general multi-input quantum networks. The construction of these inequalities relies on the number of leaf nodes, a network parameter that can be identified by a linear-time algorithm. Our approach establishes a structural connection between bipartite full-correlation Bell inequalities and network Bell inequalities, enabling the analytical derivation of optimal quantum violations and the conditions under which they occur. We further quantify the upper bound on maximal violations achievable by arbitrary two-qubit mixed states in such networks, under separable measurements, and evaluate the noise robustness of the proposed inequalities via the visibilities of noisy states. Finally, we demonstrate that these inequalities can, in a device-independent manner, distinguish between network topologies of equal size that differ in the number of leaf nodes.
Quantum networks are built from independent sources, and their nonlocality has mostly been studied with sources that emit bipartite entangled states. A source of three entangled qubits is richer, since its nonlocality can be tested by the Mermin or the more demanding Svetlichny inequality. We ask how network nonlocality relates to these two single-source notions and find that the answer depends on the wiring. When two central nodes without inputs share every source, Bell-state measurements turn every Svetlichny violation into a network violation, and even all entangled generalised Greenberger-Horne-Zeilinger states violate the network inequality. When a single central node is shared, the relation reverses, and a network violation requires a Mermin violation of the source. With more sources, the maximal violation depends on whether their number is even or odd, and we give tight bounds for both cases. These results show that the way multipartite sources are wired decides which kind of nonlocality a network inherits.