A sum rule for tidal Love number is derived from quantum field theory computations, which relates tidal susceptibility of a spinless body to transition rates of its single graviton emission processes. An analogous sum rule for electromagnetism is given as an example, which is substantiated by comparing to the solved problem of the hydrogen atom. Based on the semiclassical Hawking radiation spectrum, a finite nonvanishing value for quantum corrections to the Love number of Schwarzschild black holes in general relativity is computed using the sum rule, which is known to classically vanish.