Precision bounds for bosonic quantum batteries

We study precision charging in bosonic quantum batteries under a finite-energy constraint, using the signal-to-noise ratio (SNR) of delivered excitations as an operational metric directly tied to the energy measured at a load. At the state level, we derive a classical bound whose violation is equivalent to antibunching and certifies non-classicality, and a Gaussian bound whose violation certifies non-Gaussianity under fixed temperature and energy-input constraints. We identify experimentally accessible non-Gaussian families that surpass this Gaussian bound at finite temperature, thereby establishing non-Gaussianity as a resource for enhanced charging precision. Finally, we introduce a linear photodetection model which, under standard linear-response assumptions, propagates these bounds to the photocurrent level and enables both witnesses to be evaluated solely from electrical statistics. Together, these results provide a realistic route to demonstrating an operational quantum advantage-defined as surpassing classical and Gaussian precision bounds-in a thermodynamically motivated energy-conversion task, with plausible near-term applications to the precision charging of fragile nanoscopic loads.