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arXiv:2307.09293

Star network non-n-local correlations can resist consistency noises better

Kan He, Yueran Han

Published Jul 18, 2023• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2307.09293

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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.
Linear nnn-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-nnn-local features of quantum correlations in a noisy network scenario. In this context, persistency of non-nnn-locality has been introduced. Such a notion helps in analyzing decay of non-nnn-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.
Network nonlocality exhibits completely novel quantum correlations compared to standard quantum nonlocality. It has been shown that network nonlocality can be shared in a generalized bilocal scenario via weak measurements [Hou, Liu, and Ren, Phys. Rev. A 105, 042436 (2022)]. In this paper, we investigate network nonlocality sharing via weak measurements in a generalized star-shaped network configuration with arbitrary numbers of unbiased dichotomic input kkk, which includes nnn branches and adds $(m\ensuremath{-}1)$ more parties in each branch to the original star network (n,m=1,k=2)(n,m=1,k=2)(n,m=1,k=2) scenario. It is shown that network nonlocality sharing among all observers can be revealed from simultaneous violation of 2n{2}^{n}2n inequalities in the (n,m=2,k=2)(n,m=2,k=2)(n,m=2,k=2) and (n,m=2,k=3)(n,m=2,k=3)(n,m=2,k=3) scenarios for any nnn branches. The noise resistance of network nonlocality sharing with a precise noise model is also analyzed.
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-nnn-locality in two distinct network topologies (linear and star). We have studied the extremal violations of nnn-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-nnn-locality in a linear network. However, the same is not true for star nnn-local network. The present analysis reveals that entanglement of all the independent sources is not a necessity for generation of non-nnn-local correlations in star topology. Characterization of sources in terms of the minimum entanglement requirement for any fixed violation amount of the nnn-local inequalities is also provided. Interestingly, detection of non-nnn-locality is ensured in the network if product of concurrence of all the sources involved exceeds 12.\frac{1}{2}.21​.
The nonlocality arising in a multiparty network involving multiple independent sources radically differs from the standard multipartite Bell nonlocality involving a single source. The notion of the full network nonlocality (FNN) [A. Pozas-Kerstjens et al., Full network nonlocality, Phys. Rev. Lett. 128, 010403 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.010403] characterizes the quantum correlations that cannot be reproduced by a local-nonlocal model featuring one local source and the rest of nonlocal no-signaling sources. However, the demonstration of FNN was limited to bilocal and trilocal star-shaped network scenarios involving three or two dichotomic measurements for edge parties. In this Letter, we first demonstrate that a large class of prevailing network inequalities does not exhibit FNN. We then introduce an elegant set of arbitrary-party and unbounded-input network inequalities in star-shaped and linear-chain networks whose optimal quantum violation exhibits FNN, certifying that the nonlocality is genuinely distributed to the entire network. Contrasting to existing demonstrations of FNN that inevitably require fixed-input and four-output elegant joint measurements for the central party, our generalized inequalities are more experimentally friendly, requiring only two output measurements. Moreover, our derivation of optimal quantum violation is fully analytic and devoid of assuming the dimension of the quantum system, thereby showcasing its potential for device-independent self-testing.