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.
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 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.
Imperfections from devices can result in the decay or even vanish of non-n-local correlations as the number of parties n increases in the polygon and linear quantum networks ([Phys. Rev. A 106, 042206 (2022)] and [Phys. Rev. A 107, 032404 (2023)]). Even so this phenomenon is also for the special kind of noises, including consistency noises of a sequence of devices, which means the sequence of devices have the same probability fails to detect. However, in the paper, we discover that star network quantum non-n-local correlations can resist better consistency noises than these in polygon and linear networks. We first calculate the noisy expected value o f star network non-n-locality and analyze the persistency conditions theoretically. When assume that congener devices have the consistency noise, the persistency number of sources n has been rid of such noises, and approximates to the infinity. Polygon and linear network non-n-local correlations can not meet the requirements. Furthermore, we explore the change pattern of the maximal number of sources nmax such that non-nmax-local correlation can be demonstrated in the star network under the influence of partially consistent noises, which is more general than consistent ones.
Abstract Recently, a class of innovative notions on quantum network nonlocality (QNN), called full quantum network nonlocality (FQNN), have been proposed in Phys. Rev. Lett. 128 010403 (2022). As the generalization of full network nonlocality (FNN), l-level quantum network nonlocality (l-QNN) was defined in arxiv. 2306.15717 quant-ph (2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.
Linear n-local networks are compatible with quantum-repeater-based entanglement distribution protocols. Different sources of imperfections such as error in entanglement generation, communication over noisy quantum channels, and imperfections in measurements result in decay of quantumness across such networks. From practical perspectives it becomes imperative to analyze the nonclassicality of quantum network correlations in the presence of different types of noise. The present discussion provides a formal characterization of non-n-local features of quantum correlations in a noisy network scenario. In this context, persistency of non-n-locality has been introduced. Such a notion helps in analyzing decay of non-n-local features of network correlations with increasing length of the linear network in the presence of one or more causes of imperfections.
现实情况下，理想的量子网络并不存在，更多的是含噪声的量子网络，在噪声情况下的量子网络会随着资源数量n的增加，其非n局域性会逐渐降低。而不同量子网络中的非多局域关联在抗噪声干扰方面表现不同。所以在本文中，单独研究了噪声星型网络的非局域性情况，计算出其不等式判据，并推导出在不同噪声情况下星型网络的非局域判断标准，由此可以判断出在给定噪声参数的情况下，不同资源数的星型网络的非局域性情况。In reality, the ideal quantum network does not exist. Instead, what we have more often are quantum networks with noise. In a quantum network under noisy conditions, as the number n of resources increases, its non-n-locality will gradually decrease. Moreover, the non-multi-locality correlations in different quantum networks exhibit different performances in terms of resistance to noise interference. Therefore, in this paper, the non-locality situation of the noisy star-shaped quantum network is studied separately. The inequality criterion is calculated, and the non-locality judgment criteria for the star-shaped network under different noisy conditions are derived. Thus, it is possible to determine the non-locality situation of star-shaped networks with different numbers of resources under the given noise parameters.
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.