Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications come to high-dimensional multimeasurement scenarios, it is crucial and challenging to witness the incompatibility of measurements with complex structures. To address this problem, we propose a modified quantum state discrimination protocol that decomposes complex compatibility structures into pairwise ones and employs noise robustness to bound incompatibility structures. We then derive arithmetic bounds for arbitrary measurements and analytical bounds for mutually unbiased bases, and capture some quantum incompatibility structures where measurements are partly compatible and partly incompatible. Finally, we experimentally demonstrate our results and connect them with quantum steering, quantum simulability and quantum communications.

中文翻译：

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见证高维多测量系统中的量子不相容性结构


量子不兼容性，即无法同时执行某些量子测量的现象，对于各种量子信息处理任务（例如非局域性和转向）是必需的。当这些应用涉及到高维多测量场景时，见证测量与复杂结构的不兼容性至关重要且具有挑战性。为了解决这个问题，我们提出了一种改进的量子态判别协议，该协议将复杂的兼容结构分解为成对的结构，并对绑定不相容结构采用噪声鲁棒性。然后，我们推导出任意测量的算术边界和相互无偏基的解析边界，并捕获一些量子不相容结构，其中测量部分兼容和部分不兼容。最后，我们实验证明了我们的结果，并将它们与量子转向、量子可模拟性和量子通信联系起来。