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arXiv · 2607.02960

Full-Period Optical Phase Estimation with Heisenberg Scaling Using Displaced Squeezed States and Gaussian Measurements

Marco A. Rodríguez-García·Luis Medina-Dozal·Francisco E. Becerra
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Abstract

We propose two-stage optimized strategies for full-period optical phase estimation with single-mode Gaussian states and Gaussian measurements under a fixed energy constraint. In the first stage (Stage I), displaced squeezed probes and heterodyne measurements provide coarse localization of the phase to a window on the circle. In the second stage (Stage II), squeezed-vacuum probes with adaptive homodyne measurements perform efficient phase estimation inside the selected window. We derive a generalized Cram\'er-Rao bound for this family of two-stage Gaussian strategies, which contains the contribution from local parameter estimation in Stage II plus an overshoot penalty from coarse localization errors in Stage I. For E <= 25 photons and squeezing limited to 12 dB, protocols using displaced squeezed states in Stage I reduce the optimized two-stage bound relative to protocols using coherent states in Stage I, and remain within a factor of 3 to 30 of the idealized local squeezed-vacuum quantum Cram\'er-Rao bound.

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Marco A. Rodríguez-García, Luis Medina-Dozal, Francisco E. Becerra. 2026-07-03. Full-Period Optical Phase Estimation with Heisenberg Scaling Using Displaced Squeezed States and Gaussian Measurements. https://arxiv.org/abs/2607.02960

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