Exploring many-body interactions through quantum Fisher information

The investigation of many-body interactions holds significant importance for both quantum foundations and information. Hamiltonians coupling multiple particles at once, beyond other applications, can lead to faster entanglement generation, multiqubit gate implementation, and improved error correction. As an increasing number of quantum platforms can enable the realization of such physical settings, it has become interesting to study the verification of many-body-interaction resources. In this work, we explore the possibility of higher-order coupling detection through the quantum Fisher information. For a family of normalized symmetric k -body Isinglike Hamiltonians, we derive bounds on the quantum Fisher information in product states. Due to its ordering with respect to the order of interaction, we demonstrate the possibility of detecting many-body couplings for a given Hamiltonian from the discussed family by observing violations of an appropriate bound. As a possible extension to these observations, we further analyze an example concerning three-body-interaction detection in the XY model.