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arXiv:2503.14188 · Physical Review Letters

Optimal Moment-Based Characterization of a Gaussian State

Niels Tripier-Mondancin, Ilya Karuseichyk, Mattia Walschaers, Valentina Parigi, Nicolas Treps

Published Jul 25, 2025• 2 citations
arXivHTMLPDF

Abstract

Fast and precise characterization of Gaussian states is crucial for their effective use in quantum technologies. In this work, we apply a multiparameter moment-based estimation method that enables rapid and accurate determination of squeezing, antisqueezing, and the squeezing angle of the squeezed vacuum state. Compared to conventional approaches, our method achieves faster parameter estimation with reduced uncertainty, reaching the Cramér-Rao bound. We validate its effectiveness using the two most common measurement schemes in continuous-variable quantum optics: homodyne detection and double homodyne detection. This rapid estimation framework is well suited for dynamically characterizing sources with time-dependent parameters, potentially enabling real-time feedback stabilization.

DOI
10.1103/1kln-n48s

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Fast and precise characterization of Gaussian states is crucial for their effective use in quantum technologies. In this work, we apply a multiparameter moment-based estimation method that enables rapid and accurate determination of squeezing, antisqueezing, and the squeezing angle of the squeezed vacuum state. Compared to conventional approaches, our method achieves faster parameter estimation with reduced uncertainty, reaching the Cramér-Rao bound. We validate its effectiveness using the two most common measurement schemes in continuous-variable quantum optics: homodyne detection and double homodyne detection. This rapid estimation framework is well suited for dynamically characterizing sources with time-dependent parameters, potentially enabling real-time feedback stabilization.
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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.
Abstract Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramér–Rao bound (CRB) is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable (CV) quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.
Abstract Ideally, the characterization of non-classical states requires measurements on timescales much shorter than the system’s decoherence time. However, in quantum cavity electrodynamics, photon loss rates are often comparable to measurement rates, which degrades the fidelity of the readout. In this work, we propose an active protocol to accelerate the phase estimation of squeezed vacuum states trapped in a lossy cavity. Instead of relying on passive leakage or linear coherent driving, we excite the system with a time-optimized degenerate parametric drive. This adapted two-photon pump actively amplifies the relevant quantum fluctuations, rapidly projecting the phase information of the squeezed state onto the integrated homodyne photocurrent of the output field before significant decoherence occurs. Because a squeezed vacuum carries no phase information in its first moments, this quadratic control is the minimal resource able to imprint the squeezing angle onto the detected signal. Using a numerical optimal control approach, we derive pumping envelopes that maximize the ability to distinguish between orthogonal squeezed states, achieving approximately a 6.02-fold increase in signal contrast compared to constant excitation schemes. We demonstrate that this active extraction protocol produces a strictly monotonic calibration curve, enabling rapid and unambiguous identification of the squeezed phase angle. Furthermore, robustness analysis confirms that the phase estimate remains reliable even in the presence of intense Gaussian detection noise, providing a practical framework for rapid state verification in open-system quantum technologies.
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We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.