Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations

Abstract

This review offers a comprehensive exploration and synthesis of recent advancements in the domain of quantum correlation sharing facilitated through sequential measurements. We initiate our inquiry by delving into the interpretation of the joint probability, laying the foundation for an examination of quantum correlations within the context of specific measurement methods. The subsequent section meticulously explores nonlocal sharing under diverse measurement strategies and scenarios, with a specific focus on investigating the impact of these strategies on the dissemination of quantum nonlocality. Key perspectives such as "asymmetry" and "weak value" are scrutinized through detailed analyses across various scenarios, allowing us to evaluate the potential of nonlocality sharing. We also provide a retrospective overview of experimental endeavors associated with this phenomenon. The third part of our exploration presents research findings on steering sharing, offering clarity on the feasibility of steering sharing and summarizing the distinctive properties of quantum steering sharing in different scenarios. Continuing our journey, the fourth section delves into discussions on the sharing of diverse quantum correlations, encompassing network nonlocality, quantum entanglement, and quantum contextuality. Moving forward, the fifth section conducts a comprehensive review of the progress in the application of quantum correlation sharing, specifically based on sequential measurement strategies. Applications such as quantum random access coding, random number generation, and self-testing tasks are highlighted. Finally, we discuss and list some of the key unresolved issues in this research field, and conclude the entire article.

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• Robust device-independent characterization of sharpness and incompatibility of unsharp instruments
• Local-available quantum correlation swapping in one-parameter X states