The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as the quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question as to how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce an approach to prove the generic activated nonlocality as a result of entanglement swapping for all the bipartite entangled states. The result is further applied to show the multipartite nonlocality and activated nonlocality for all the nontrivial quantum networks consisting of any entangled states. Our results provide the nonlocality witnesses and quantum superiorities of all the connected quantum networks or nontrivial hybrid networks in contrast to classical networks.
A quantum network consists of independent sources distributing entangled states to distant nodes which can then perform entangled measurements, thus establishing correlations across the entire network. But how strong can these correlations be? Here we address this question, by deriving bounds on possible quantum correlations in a given network. These bounds are nonlinear inequalities that depend only on the topology of the network. We discuss in detail the notably challenging case of the triangle network. Moreover, we conjecture that our bounds hold in general no-signaling theories. In particular, we prove that our inequalities for the triangle network hold when the sources are arbitrary no-signaling boxes which can be wired together. Finally, we discuss an application of our results for the device-independent characterization of the topology of a quantum network.
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.Large-scale quantum networks have been employed to overcome practical constraints of transmission and storage for single entangled systems. Our goal in this paper is to explore the strong entanglement distribution of quantum networks. We firstly show that any connected network consisting of generalized Einstein-Podolsky-Rosen states and Greenberger-Horne-Zeilinger states satisfies the strong Coffman-Kundu-Wootters monogamy inequality in terms of the bipartite entanglement measure; in addition, the monogamy inequalities are also considered for generic entangled quantum networks. This reveals the interesting feature of high-dimensional entanglement with local tensor decomposition going beyond qubit entanglement. We then apply the entanglement distribution relation in entangled networks to get a quantum maximum-flow minimum-cut theorem in terms of von Neumann entropy and R\'enyi-$\ensuremath{\alpha}$ entropy. We finally classify entangled quantum networks by distinguishing network configurations under local unitary operations. These results provide insights into characterizing quantum networks in quantum information processing.
Entangled systems in experiments may be lost or off-line in distributed quantum information processing. This inspires a general problem to characterize quantum operations, which result in breaking of entanglement or not. Our goal in this paper is to solve this problem both in single entanglement and network scenarios. We firstly propose a local model for characterizing all entangled states that are breaking for losing particles. This implies a simple criterion for witnessing single entanglement such as generalized GHZ states and Dicke states. It further provides an efficient witness for entangled quantum networks depending on its connectivity such as
k-independent quantum networks, completely connected quantum networks, and
k-connected quantum networks. These networks are universal resources for measurement-based quantum computations. The strong nonlocality can be finally verified by using nonlinear inequalities. These results show distinctive features of both single entangled systems and entangled quantum networks.
Analyzing the nonclassicality of correlations generated in
n-local quantum networks is an important branch of study in quantum information theory. Speaking of nonclassicality, violation of an
n-local inequality ensures non
n-locality of corresponding network correlations. Being correlation-based, violation of any such inequality is experimentally feasible. The present work explores whether applying suitable local unitary operations can aid violation of any
n-local inequality. Observations have ensured the utility of local unitary operations in enhancing the detection efficiency of bilocal inequality and
n-local inequality (for
n=3,4) in the star configuration. In an
n-local quantum network, such operations correspond to local basis change applied by at least one party over its joint state of qubits received from the sources. In an
n-local network, with all the parties performing any possible local unitary operation, correlations not violating an
n-local inequality (compatible with the network considered), are first characterized. Such characterization is then exploited to provide examples of local unitary operations aiding violation of existing
n-local inequalities for
n=2, 3, and 4, specifically. Interestingly, there exist two qubit unitary operations, for which nontrilocal correlations can be simulated even when one of the sources distribute pure product state in star network. Quantum gates associated with the useful unitary operations are provided.