A review of quantum correlation sharing: The recycling of quantum correlations triggered by quantum measurements

Quantum correlation and quantum measurement are core issues in understanding the quantum world. Revealing quantum correlations in microphysical systems through proper quantum measurements became an important research topic in the last century and gave rise to the birth of quantum information technologies. However, quantum correlations, quantum measurements, and their relationship are not yet fully understood and require further clarification. The development of generalized quantum measurement and non-destructive measurement provides new possibilities for studying these issues. In the past decade, a series of studies on quantum correlation sharing through sequential generalized measurements have unveiled a new avenue for exploring quantum correlations. These studies not only have important fundamental significance, but also involve the unexplored issue of quantum resource recycling. This review thoroughly examines recent advancements in quantum correlation sharing. It begins by elucidating the fundamental reasons for quantum correlation sharing based on the interpretation of joint probabilities, and discussing the basic definitions and concepts. Next, the sharing of Bell nonlocality under different measurement strategies and scenarios is carefully examined, especially pointing out the impact of these strategies on the maximum number of parties that can exhibit Bell nonlocality. The subsequent chapters provide an overview of other forms of quantum correlation sharing, including quantum steering, network nonlocality, quantum entanglement, and quantum contextuality. Furthermore, we summarize the advancements in the application of quantum correlation sharing across various quantum tasks, highlighting examples such as quantum random access codes, random number generation, and self-testing tasks. Finally, we discuss and enumerate some key unresolved issues in this research area, concluding this review.