Abstract Quantum networks with multiple sources always face performance challenges due to the vulnerability of quantum systems. Thus, it is highly desirable to have the capability to continuously monitor and determine the exact number of quantum sources versus classical sources present within the network. Hierarchical network nonlocality can reveal the relationship between network nonlocality and the number of quantum sources within the network, thus becoming a way to address the aforementioned issue. However, up to now, precise hierarchical network nonlocality inequalities have only been established for star networks, and cannot be obtained for other non-star structured networks [Phys. Rev. Lett. 128 010403 (2022) and Phys. Rev. A 110 022617 (2024)]. In this paper, we establish more refined criteria for hierarchical network nonlocality inequalities in arbitrary network structures. Violating such inequalities can reveal the exact number of quantum sources in the network. These results enhance the understanding of quantum source distribution in complex network topologies.
Abstract Quantum networks with multiple sources always face performance challenges due to the vulnerability of quantum systems. Thus, it is highly desirable to have the capability to continuously monitor and determine the exact number of quantum sources versus classical sources present within the network. Hierarchical network nonlocality can reveal the relationship between network nonlocality and the number of quantum sources within the network, thus becoming a way to address the aforementioned issue. However, up to now, precise hierarchical network nonlocality inequalities have only been established for star networks, and cannot be obtained for other non-star structured networks [Phys. Rev. Lett. 128 010403 (2022) and Phys. Rev. A 110 022617 (2024)]. In this paper, we establish more refined criteria for hierarchical network nonlocality inequalities in arbitrary network structures. Violating such inequalities can reveal the exact number of quantum sources in the network. These results enhance the understanding of quantum source distribution in complex network topologies.
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.
Source-independent quantum networks are considered as a natural generalization to the Bell scenario where we investigate the nonlocal properties of quantum states distributed and measured in a network. Considering the simplest network of entanglement swapping, recently Gisin et al. [Phys. Rev. A 96, 020304(R) (2017)] and Andreoli [New. J. Phys. 19, 113020 (2017)] independently provided a systematic characterization of the set of quantum states leading to violation of the so-called bilocality inequality. In this work, we consider the complexities in quantum networks with an arbitrary number of parties distributed in chain-shaped and star-shaped networks. We derive the maximal violation of the ``n-local'' inequality that can be achieved by arbitrary two-qubit states for such chain- and star-shaped networks. This would further provide a deeper understanding of quantum correlations in complex structures.
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.
ABSTRACT Full quantum network nonlocality (FQNN) is an innovative perspective which signifies that all sources within the network exhibit quantum characteristics. So far, FQNN has been certified by violating a single Bell‐like inequality, but only for star networks. No such test exists for general topologies. (Luo et al., Phys. Rev. A 110, 022617 (2024)) suggested iterating the FQNN criteria of star networks to cover general networks, since any general network can be decomposed into a collection of star subnetworks. However, this method requires a large number of inequalities for large networks. This paper aims to clarify how a smaller set of Bell‐like inequalities can be employed to detect FQNN in general networks. By exploiting the structural features of the network, we derive a new class of inequalities. Violations of these inequalities reveal the locations of several quantum sources, enabling the detection of overall FQNN with fewer tests. We demonstrate the advantage of our approach explicitly for two types of networks, ‐layer ‐forked tree‐shaped and Bethe lattice networks. We demonstrate an exponential reduction in the number of Bell‐like inequalities required to witness FQNNs on these two types of networks.
Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.
With the increased availability of quantum technological devices, it becomes more important to have tools to guarantee their correct nonclassical behavior. This is especially important for quantum networks, which constitute the platforms where multipartite cryptographic protocols will be implemented, and where guarantees of nonclassicality translate into security proofs. We derive linear and nonlinear Bell-like inequalities for networks, whose violation certifies the absence of a minimum number of classical sources in them. We do so, first, without assuming that nature is ultimately governed by quantum mechanics, providing a hierarchy interpolating between network nonlocality and full network nonlocality. Second we insert this assumption, which leads to results more amenable to certification in experiments.