  Achieving the ultimate precisions for multiple parameters simultaneously is
an outstanding challenge in quantum physics, because the optimal measurements
for incompatible parameters cannot be performed jointly due to the Heisenberg
uncertainty principle. In this work, a criterion proposed for multiparameter
estimation provides a possible way to beat this curse. According to this
criterion, it is possible to mitigate the influence of incompatibility
meanwhile improve the ultimate precisions by increasing the variances of the
parameter generators simultaneously. For demonstration, a scheme involving
high-order Hermite-Gaussian states as probes is proposed for estimating the
spatial displacement and angular tilt of light at the same time, and precisions
up to 1.45 nm and 4.08 nrad are achieved in experiment simultaneously.
Consequently, our findings provide a deeper insight into the role of Heisenberg
uncertainty principle in multiparameter estimation, and contribute in several
ways to the applications of quantum metrology.
