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Fadel, M., Roux, N., & Gessner, M. (2025). Quantum metrology with a continuous-variable system. Rep. Prog. Phys., 88(10), 106001–46pp.
Abstract: As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and the design of optimized measurement observables. We discuss precision limits and optimal strategies in quantum metrology and sensing with a single mode of quantum continuous variables. We focus on the practically most relevant cases of estimating displacements and rotations and provide the sensitivities of the most important classes of states that includes Gaussian states and superpositions of Fock states or coherent states. Fundamental precision limits that are obtained from the quantum Fisher information are compared to the precision of a simple moment-based estimation strategy based on the data obtained from possibly sub-optimal measurement observables, including homodyne, photon number, parity and higher moments. Finally, we summarize some of the main experimental achievements and present emerging platforms for continuous-variable sensing. These results are of particular interest for experiments with quantum light, trapped ions, mechanical oscillators, and microwave resonators.
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Fadel, M., Yadin, B., Mao, Y. P., Byrnes, T., & Gessner, M. (2023). Multiparameter quantum metrology and mode entanglement with spatially split nonclassical spin ensembles. New J. Phys., 25(7), 073006–25pp.
Abstract: We identify the multiparameter sensitivity of entangled spin states, such as spin-squeezed and Dicke states that are spatially distributed into several addressable spatial modes. Analytical expressions for the spin-squeezing matrix of families of states that are accessible by current atomic experiments reveal the quantum gain in multiparameter metrology, as well as the optimal strategies to maximize the sensitivity gain for the estimation of any linear combination of parameters. We further study the mode entanglement of these states by deriving a witness for genuine k-partite mode entanglement from the spin-squeezing matrix. Our results highlight the advantage of mode entanglement for distributed sensing, and outline optimal protocols for multiparameter estimation with nonclassical spatially-distributed spin ensembles. We illustrate our findings with the design of a protocol for gradient sensing with a Bose-Einstein condensate in an entangled spin state in two modes.
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Liu, X. Z., Yang, Y. H., Gessner, M., Smerzi, A., Li, W. D., Yang, X., et al. (2025). Photonic Metrology with Hierarchic Quantum Frequentist Bounds. Adv. Photon. Res., , 7pp.
Abstract: Quantum metrology establishes fundamental precision limits for parameter estimation, yet standard Quantum Cram & eacute;r-Rao Bound (QCRB) becomes insufficient in the finite-data regime. In this article, the QCRB is systematically tighten using a hybrid classical-quantum framework by incorporating generalized unbiasedness constraints through test observables. These frequentist bounds form a hierarchy converging asymptotically to the QCRB as more measurements are performed. These hierarchical frequentist bounds are validated for single-qubit phase estimation on a photonic platform.
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Sorelli, G., Gessner, M., Treps, N., & Walschaers, M. (2024). Gaussian quantum metrology for mode-encoded parameters. New J. Phys., 26(7), 073022–23pp.
Abstract: Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes.
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