Sharing quantum nonlocality in star network scenarios

Abstract

The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.

Graphical abstract

Keywords

Bell nonlocality / quantum network / nonlocality sharing / POVM measurements

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Note added

While completing this manuscript, we became aware of Refs. [68-70] studied the same topic and got similar results. However, we all used different methods. Compared with our strict theoretical proofs, Ref. [68] used symmetric and anti-symmetric methods, Ref. [69] mainly used weak measurement theory, Ref. [70] focused on experimental simulation.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 12126314, 12126351, 11861031, 12075159, and 12171044; the Hainan Provincial Natural Science Foundation of China under Grant No. 121RC539, the Specific Research Fund of the Innovation Platform for Academicians of Hainan Province under Grant No. YSPTZX202215, Beijing Natural Science Foundation (Grant No. Z190005); Academy for Multidisciplinary Studies, Capital Normal University; Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology (No. SIQSE202001).

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