1. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China 2. College of Sciences, Shanghai University, Shanghai 200444, China 3. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA 4. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China 5. Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
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.
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