Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements

The incompatibility of the optimal measurements for the estimation of different parameters constraints the achievable precisions in multi-parameter quantum estimation. Understanding the tradeoff induced by such incompatibility is thus a central topic in quantum metrology. Here we provide an approach to study the incompatibility in terms of information geometry under general p-local measurement, which are the measurements performed collectively on at most p copies of quantum states. We demonstrate the power of the approach by present a hierarchy of analytical tradeoff relations induced by the incompatibility.