Phase estimation plays a central role in communications, sensing, and information processing. Here, we propose a novel adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states with precision close to the quantum limit. By constructing a comprehensive set of locally optimal positive operator-valued measures (POVMs) through rotations and homodyne measurements, our approach optimizes the adaptive measurement process using the complete homodyne measurement records. This adaptive phase estimation strategy outperforms previous approaches for phase estimation and approaches the quantum limit within the phase interval of [0,π/2). We further generalize this adaptive strategy to incorporate heterodyne measurements, enabling near quantum-limited precision for phase estimation across the entire range of phases from [0,π). Remarkably, our proposed strategy approaches an asymptotic optimal performance in this phase interval, which corresponds the maximum range of phases that can be unambiguously encoded in squeezed vacuum states.
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