Quantum network correlations have attracted strong interest because they may reveal new types of locality violations. Here we investigated network nonlocality sharing in the extended bilocal scenario via weak measurements, which adds one more observer to either end of the well-known entanglement-swapping scenario. Intriguingly, network nonlocality sharing can be revealed from the multiple violation of the Branciard-Rosset-Gisin-Pironio inequality by considering two contrasting motivations of intermediate observers, which has no counterpart in standard Bell scenarios. In addition, the noise resistance of network nonlocality sharing was also discussed.
Quantum network correlations have attracted strong interest because they may reveal new types of locality violations. Here we investigated network nonlocality sharing in the extended bilocal scenario via weak measurements, which adds one more observer to either end of the well-known entanglement-swapping scenario. Intriguingly, network nonlocality sharing can be revealed from the multiple violation of the Branciard-Rosset-Gisin-Pironio inequality by considering two contrasting motivations of intermediate observers, which has no counterpart in standard Bell scenarios. In addition, the noise resistance of network nonlocality sharing was also discussed.
Quantum networks, which can exceed the framework of standard bell theorem, flourish the investigation of quantum nonlocality further. Recently, a concept of full quantum network nonlocality (FNN) which is stronger than network nonlocality, has been defined and can be witnessed by Kerstjens-Gisin-Tavakoli (KGT) inequalities [Phys. Rev. Lett. 128 (2022)]. In this letter, we explored the recycling of FNN as quantum resources by analyzing the FNN sharing between different combinations of observers. The FNN sharing in extended bilocal scenario via weak measurements has been completely discussed. According to the different motivations of the observer-Charlie1, two types of possible FNN sharing, passive FNN sharing and active FNN sharing, can be investigated by checking the simultaneous violation of KGT inequalities between Alice-Bob-Charlie1 and Alice-Bob- Charlie2. Our results show that passive FNN sharing is impossible while active FNN sharing can be achieved by proper measurements, which indicate that FNN sharing requires more cooperation by the intermediate observers compared with Bell nonlocal sharing and network nonlocal sharing.
Abstract The investigation of network nonlocality (NN) has expanded the study of quantum nonlocality, yet it fails to fully capture the complexities within quantum networks. Recently, a stronger and more genuine definition of NN, known as full quantum network nonlocality (FNN), has been explored, which is considered a vital resource for realizing network-based device-independent quantum cryptography protocols. In this work, we explore the recycling of FNN as quantum resources by analyzing the FNN sharing between different combinations of observers. The FNN sharing in an extended bilocal scenario (consisting of two independent two-qubit quantum states as sources) via weak measurements has been thoroughly discussed. Based on the different motivations of the observer-Charlie1, two types of possible FNN sharing, passive FNN sharing and active FNN sharing, can be investigated by checking the simultaneous violation of Kerstjens–Gisin–Tavakoli inequalities between Alice-Bob-Charlie1 and Alice-Bob-Charlie2. Our results show that passive FNN sharing is impossible while active FNN sharing can be achieved through proper measurements, indicating that FNN sharing in this scenario requires more cooperation by intermediate observers compared to Bell nonlocality sharing and NN sharing.
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 k, which includes n branches and adds $(m\ensuremath{-}1)$ more parties in each branch to the original star network (n,m=1,k=2) scenario. It is shown that network nonlocality sharing among all observers can be revealed from simultaneous violation of 2n inequalities in the (n,m=2,k=2) and (n,m=2,k=3) scenarios for any n branches. The noise resistance of network nonlocality sharing with a precise noise model is also analyzed.
In an entanglement swapping scenario, if two sources distributing entangled states between three parties are independent, local correlations lead to a different kind of inequality than the standard Bell inequalities, known as network local models. A highly demanding task is to find out a way to involve many players nontrivially in a quantum network since measurements, in general, disturb the system. To this end, we consider here an alternative way of sharing network nonlocality when two observers initially share a maximally entangled, a nonmaximally entangled and a noisy entangled state. We report that by employing unsharp measurements performed by one of the observers, at most six pairs can sequentially demonstrate the violation of bilocal inequality while a maximum of two pairs of observers can exhibit bi-nonlocality when both the observers perform unsharp measurements. We also find the critical noise involved in unsharp measurements in each round to illustrate the bi-nonlocality for a fixed shared entangled state as a resource. We also connect the entanglement content of the shared state, quantified via von-Neumann entropy for pure states and entanglement of formation for Werner states with the maximum number of rounds showing violation of bilocal inequality. By considering elegant joint measurement at the node such that the entanglement content in the elements of the joint measurement by the third party gets reduced, we observe that the maximum number reduces to two sequential sharing of bi-nonlocality even for the maximally entangled state when the settings at each side are taken to be three and fixed.
Nonlocality arising in networks composed of several independent sources gives rise to phenomena radically different from that in standard Bell scenarios. Over the years, the phenomenon of network nonlocality in the entanglement-swapping scenario has been well investigated and demonstrated. However, it is known that violations of the so-called bilocality inequality used in previous experimental demonstrations cannot be used to certify the nonclassicality of their sources. This has put forward a stronger concept for nonlocality in networks, called full network nonlocality. Here, we experimentally observe full network nonlocal correlations in a network where the source-independence, locality, and measurement-independence loopholes are closed. This is ensured by employing two independent sources, rapid setting generation, and spacelike separations of relevant events. Our experiment violates known inequalities characterizing nonfull network nonlocal correlations by over 5 standard deviations, certifying the absence of classical sources in the realization.
The multipartite quantum networks feature multiple independent sources, in contrast to the conventional multipartite Bell experiment involving a single source. Despite the initial independence of resources, the multiple observers in the network can suitably choose measurements on their local subsystems and generate a form of quantum nonlocality across the network. So far, network nonlocality has been explored when each source produces a two-qubit entangled state. In this work we demonstrate the network nonlocality when each party performs a black-box measurement, and the dimension of the system remains unspecified. In an interesting work, by considering each source produces two-qubit entangled states in the conventional bilocal scenario, Gisin et al. [Phys. Rev. A 96, 020304 (2017)] demonstrated a correspondence between the violations of bipartite Clauser-Horne-Shimony-Halt inequality and the bilocality inequality. We introduce a variant of the sum-of-squares approach to reproduce their results without assuming the dimension of the system. We then generalize the argument for network nonlocality in star-network topology. Furthermore, we propose a set of n-locality inequalities in a star-network configuration where each of the n parties performs an arbitrary number of dichotomic measurements and demonstrates the above correspondence between the quantum violations of the n-locality inequalities and the chained Bell inequalities. A similar correspondence is demonstrated based on a recently formulated family of n-locality inequalities whose optimal quantum violation cannot be obtained when each source emits a two-qubit entangled state and requires multiple copies of two-qubit entangled states. Throughout this paper, each party in the network performs black-box measurements, and the dimension of the system remains unspecified.