Abstract
The incompatibility of the measurements constraints the achievable precisions in multi-parameter quantum estimation. Understanding the tradeoff induced by such incompatibility is a central topic in quantum metrology. Here we provide an approach to study the incompatibility under general p-local measurements, which are the measurements that can be performed collectively on at most p copies of quantum states. We demonstrate the power of the approach by presenting a hierarchy of analytical bounds on the tradeoff among the precision limits of different parameters. These bounds lead to a necessary condition for the saturation of the quantum Cram\'er-Rao bound under p-local measurements, which recovers the partial commutative condition at p=1 and the weak commutative condition at p=∞. As a further demonstration of the power of the framework, we present another set of tradeoff relations with the right logarithmic operators(RLD).