A limit formula for the quantum fidelity

Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. By using the notion of generalized overlap, which occurs in the definition of the quantum Chernoff bound, we propose here a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an application, we apply this formula to the case of multimode Gaussian states, achieving a simple expression in terms of their first- and second-order statistical moments.