Pump quantization changes optimal measurements for quantum sensing

arXiv:2611.03943v1 Announce Type: new Abstract: Standard analyses of quantum phase sensing often neglect the overhead of generating squeezed-light by treating the pump as an undepleted classical resource. Realistically, the pump is a quantum object that undergoes significant depletion and entangles with the produced squeezed light, raising the question of how the crossover from a classical to a quantum pump limits the quantum advantage in sensing. Contrary to prior analyses, we show that quantum advantage persists despite pump quantization, but depends critically on the nonlinear $(\chi^{(2)})$ source dynamics. In particular, we demonstrate that Heisenberg scaling emerges in the regime of strong pump depletion, rather than maximum signal squeezing.