Witnessing Quantum Incompatibility Structures in High-Dimensional Multimeasurement Systems

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.