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.
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.
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 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 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.
Keeping pace with technological advancement, in the past decade, use of scalable networks have extended the study of quantum non-classicality beyond the regime of Bell-CHSH nonlocality. Present work provide characterization of non n-locality that can be exploited by incorporating filtering operations in star-shaped n-local networks. This in turn provide a framework of sequential n-local networks capable of generating non n-local correlations by involving some suitable form of stochastic local operations assisted with classical communications(SLOCC). It is observed that for effectiveness of such sequential networks, Bell-CHSH nonlocality(upto SLOCC operations) of every individual two-qubit state, distributed in the network, is not mandatory. However, there does not exist any separable local filter, which when applied in n-local network involving only Bell local states(upto SLOCC operations), can reveal non n-locality. Interestingly, instances revealing advantage of nonseparable mutli-qubit local filters over separable mutli-qubit local filters(by central node) are obtained. Such an advantage is attributable to the specific topology of star-shaped n-local networks and thus can never be reflected in Bell scenario.
Abstract The interest in quantum network correlations has surged, as Bell inequalities originating from a single source fall short of capturing the intricate many-body correlations within generic quantum networks. The introduction of a 3-grade m-star quantum network, a natural extension of star-shaped networks, features a hierarchy of nodes including A, m stars B 1, …, B m centered around A, and m stars C 1 j , … , C m j centered around each B j , and m + m 2 independent sources. The strong locality of this network has been explored, assuming that each party possesses only two observables. In this paper, we put forward a significant extension to the strong locality of 3-grade m-star quantum networks. Specifically, each C j k performs n dichotomic measurements, while A and each B j conduct 2 n−1 dichotomic measurements. We establish a generalized strong locality inequality that holds for any value of n, and subsequently conduct a thorough analysis to determine the optimal quantum violation of established inequality. Through specific examples, we confirm the feasibility of achieving the optimal quantum violation of the generalized strong locality inequality for any n. We notice that for n > 3, a single copy of a two-qubit entangled state may not be sufficient to reveal the non-strong locality, whereas utilizing multiple copies can trigger this property.
Entanglement and nonlocality are two important nonclassical features of quantum correlations. Recently the study of quantum correlations in networks has undergone remarkable progress owing to technological development towards scalable quantum networks. However, compared to the standard Bell scenario, manifestation of the interplay between these two aspects has received less attention in network scenarios featuring independent sources. In this work we have analyzed the relation between entanglement content of the sources and detectable non-n-locality in two distinct network topologies (linear and star). We have studied the extremal violations of n-local inequalities (compatible with linear and star network) for any fixed amount of entanglement (in terms of concurrence) of the independent sources. It is observed that each of the sources must be entangled for detecting non-n-locality in a linear network. However, the same is not true for star n-local network. The present analysis reveals that entanglement of all the independent sources is not a necessity for generation of non-n-local correlations in star topology. Characterization of sources in terms of the minimum entanglement requirement for any fixed violation amount of the n-local inequalities is also provided. Interestingly, detection of non-n-locality is ensured in the network if product of concurrence of all the sources involved exceeds 21.