Full network nonlocality sharing in extended bilocal scenario via weak measurements with the optimal pointer

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.