Efficient detection of the Quantum Fisher Information

Quantum Information geometry allows to visualize states and operations as geometric entities. 

In particular, the Quantum Fisher Information, which quantifies the sensitivity of a state to small perturbations, plays an important role in quantum information and quantum metrology. Yet, its calculation requires full knowledge of the state, which is often not achievable in the laboratory. I introduce a lower bound to the Quantum Fisher Information which can be evaluated by a limited number of interferometric measurements as well as alternative schemes. I show that the lower bound still captures important properties of the state as coherence and entanglement.