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arXiv:2310.08856 · Optics Communications

Two-parameter estimation with single squeezed-light interferometer via double homodyne detection

Li-Li Hou, Jiandong Zhang, Kaimin Zheng, Shuai Wang

Published Jul 24, 2024• 3 citations
arXivHTMLPDF
DOI
10.1016/j.optcom.2024.130898

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Abstract Performing homodyne detection at a single output port of a squeezed-state light interferometer and then separating the measurement quadrature into two intervals can realize super-resolving and super-sensitive phase measurements, which is equivalent to a binary-outcome measurement. Obviously, the single-port homodyne detection may lose almost part of the phase information, reducing the estimation precision. Here, we propose a data-processing technique over the double-port homodyne detection, where the two-dimensional measurement quadrature (p 1, p 2) has been divided into two regions. With such a binary-outcome measurement, we estimate the phase shift accumulated in the interferometer by inverting the output signal. By analyzing the full width at half maximum of the signal and the phase sensitivity, we show that both the resolution and the achievable sensitivity are better than that of the previous binary-outcome scheme.
We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by a laser and a nonlinear optical medium with passive optimal elements, which are readily available in the laboratory: One is a two-mode separable coherent and squeezed vacuum state at a beam splitter and the other is a two-mode squeezed vacuum state. In view of the ultimate precision given by quantum Fisher information, we show that the two-mode squeezed vacuum state can achieve a lower bound of estimation error than the coherent and squeezed vacuum state under a photon-loss channel. We further consider practical measurement schemes, homodyne detection and photon number resolving detection (PNRD), to characterize the accuracy of phase estimation in reality and find that the coherent and squeezed vacuum state largely achieves a lower bound than the two-mode squeezed vacuum in the lossy MZI while maintaining quantum enhancement over the shot-noise limit. By comparing homodyne detection and PNRD, we demonstrate that quadrature measurement with homodyne detection is more robust against photon loss than parity measurement with PNRD. We also show that double homodyne detection can provide a better tool for phase estimation than single homodyne detection against photon loss.
Abstract We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo Cramér–Rao bound (HCRB) for both displacement and squeezing parameter characterizing single and two-mode squeezed states. In the single-mode scenario, we obtain an analytical bound and find that it degrades monotonically as the squeezing increases. Furthermore, we prove that heterodyne detection is nearly optimal in the large squeezing limit, but in general the optimal measurement must include non-Gaussian resources. On the other hand, in the two-mode setting, the HCRB improves as the squeezing parameter grows and we show that it can be attained using double-homodyne detection.