“…Since the generators for linear and nonlinear phase accumulation are quite different, the corresponding optimized input states make huge differences. Recent interest has moved to examine the role of nonlinear interaction in the phase accumulation [34,[44][45][46], which requires different optimization strategies. However, due to the difficulties of preparing optimal input entangled states and manipulating the nonlinear phase accumulation, the experimental demonstrations of parameter estimation with nonlinear phase accumulation are still rare [24][25][26][27].…”