Nonlocal Sharing of Maximally Entangled Qubits Under Measurement Dependence

Abstract

In recent years, quantum nonlocality sharing has attracted widespread research attention. Nevertheless, all existing investigations are built upon the measurement independence assumption. The freedom‑of‑choice loophole originates when measurement settings and hidden variables cannot be guaranteed independent, which corresponds to the regime where the measurement independence assumption no longer holds. This paper pioneers the exploration of quantum nonlocality sharing under measurement-dependent scenarios. By integrating the inherent characteristics of measurement dependence with the optimization of measurement strategies for nonlocality sharing, and quantifying the performance of sequential-measurement-based nonlocality sharing via the experimental occurrence frequency of measurement dependence, we demonstrate that maintaining a certain degree of partial measurement independence is critical to achieving valid nonlocality sharing. Moreover, we analyze the correlation constraints imposed by measurement-dependent local models and clarify the physical boundary between correlations explainable by classical hidden-variable descriptions and those that cannot be reproduced by such models.