  Phase estimation plays a central role in communications, sensing, and
information processing. Quantum correlated states, such as squeezed states,
enable phase estimation beyond the shot-noise limit, and in principle approach
the ultimate quantum limit in precision, when paired with optimal quantum
measurements. However, physical realizations of optimal quantum measurements
for optical phase estimation with quantum correlated states are still unknown.
Here we address this problem by introducing an adaptive Gaussian measurement
strategy for optical phase estimation with squeezed vacuum states that, by
construction, approaches the quantum limit in precision. This strategy builds
from a comprehensive set of locally optimal POVMs through rotations and
homodyne measurements and uses the Adaptive Quantum State Estimation framework
for optimizing the adaptive measurement process, which, under certain
regularity conditions, guarantees asymptotic optimality for this quantum
parameter estimation problem. As a result, the adaptive phase estimation
strategy based on locally-optimal homodyne measurements achieves the quantum
limit within the phase interval of $[0, \pi/2)$. Furthermore, we generalize
this strategy by including heterodyne measurements, enabling phase estimation
across the full range of phases from $[0, \pi)$, where squeezed vacuum allows
for unambiguous phase encoding. Remarkably, for this phase interval, which is
the maximum range of phases that can be encoded in squeezed vacuum, this
estimation strategy maintains an asymptotic quantum-optimal performance,
representing a significant advancement in quantum metrology.
