Baamara, Y., Gessner, M., & Sinatra, A. (2023). Quantum-enhanced multiparameter estimation and compressed sensing of a field. SciPost Phys., 14(3), 050–18pp.
Abstract: We show that a significant quantum gain corresponding to squeezed or over-squeezed spin states can be obtained in multiparameter estimation by measuring the Hadamard coefficients of a 1D or 2D signal. The physical platform we consider consists of twolevel atoms in an optical lattice in a squeezed-Mott configuration, or more generally by correlated spins distributed in spatially separated modes. Our protocol requires the possibility to locally flip the spins, but relies on collective measurements. We give examples of applications to scalar or vector field mapping and compressed sensing.
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Barral, D., Isoard, M., Sorelli, G., Gessner, M., Treps, N., & Walschaers, M. (2024). Metrological detection of entanglement generated by non-Gaussian operations. New J. Phys., 26(8), 083012–20pp.
Abstract: Entanglement and non-Gaussianity are physical resources that are essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of non-Gaussian entanglement generated by multiple photon-subtraction and that it is experimentally feasible through homodyne detection.
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Biagi, N., Francesconi, S., Gessner, M., Bellini, M., & Zavatta, A. (2022). Remote Phase Sensing by Coherent Single Photon Addition. Adv. Quantum Technol., 5(12), 2200039–9pp.
Abstract: A remote phase sensing scheme is proposed, inspired by the high sensitivity of the entanglement produced by coherent multimode photon addition on the phase set in the remote heralding apparatus. By exploring the case of delocalized photon addition over two modes containing identical coherent states, the optimal observable to perform remote phase estimation from heralded quadrature measurements is derived. The technique is experimentally tested with calibration measurements and then used for estimating a remote phase with a sensitivity that is found to scale with the intensity of the local coherent states, which never interacted with the sample.
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Centrone, F., & Gessner, M. (2024). Breaking local quantum speed limits with steering. Phys. Rev. Res., 6(4), L042067–5pp.
Abstract: We show how quantum correlations allow us to break the local speed limits of physical processes using only local measurements and classical communication between two parties that share an entangled state. Inequalities that bound the minimal time of evolution of a quantum state by energy fluctuations can be violated in the presence of steering by conditioning on the measurement outcomes of a remote system. Our results open up pathways for studying how quantum correlations influence the dynamical properties of states and observables.
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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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Gebhart, V., Gessner, M., & Smerzi, A. (2024). Fundamental bounds for parameter estimation with few measurements. Phys. Rev. Res., 6(4), 043261–6pp.
Abstract: Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or low signal-to-noise ratios, the meaning of common frequentist bounds, such as the Cram & eacute;r-Rao bound (CRB), becomes questionable. Here, we discuss a different (Barankin-like) approach to derive the conditions for the existence of optimal estimators and calculate their variance, for any number of measurement repetitions. We elaborate on connections to the shot-noise limit and the Kitaev phase estimation algorithm and derive an extended Cram & eacute;r-Rao bound that is compatible with a finite variance in situations where the Barankin bound (BaB) is undefined. Finally, we show an exemplary numerical confrontation between frequentist and Bayesian approaches to parameter estimation.
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Gessner, M., & Smerzi, A. (2023). Hierarchies of Frequentist Bounds for Quantum Metrology: From Cramer-Rao to Barankin. Phys. Rev. Lett., 130(26), 260801–6pp.
Abstract: We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cramer-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.
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Gessner, M., Treps, N., & Fabre, C. (2023). Estimation of a parameter encoded in the modal structure of a light beam: a quantum theory. Optica, 10(8), 996–999.
Abstract: Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a “mode parameter” that determines properties such as frequency, temporal shape, and the spatial distribution of the light field. By deriving quantum precision limits, we establish the fundamental bounds for mode parameter estimation. Our results reveal explicit mode-design recipes that enable the estimation of any mode parameter with quantum enhanced precision. Our approach provides practical methods for optimizing mode parameter estimation with relevant applications, including spatial and temporal positioning, spectroscopy, phase estimation, and superresolution imaging.
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Guo, J. J., Sun, F. X., Zhu, D. Q., Gessner, M., He, Q. Y., & Fadel, M. (2023). Detecting Einstein-Podolsky-Rosen steering in non-Gaussian spin states from conditional spin-squeezing parameters. Phys. Rev. A, 108(1), 012435–7pp.
Abstract: We present an experimentally practical method to reveal Einstein-Podolsky-Rosen (EPR) steering in non-Gaussian spin states by exploiting a connection to quantum metrology. Our criterion is based on the quantum Fisher information, and uses bounds derived from generalized spin-squeezing parameters that involve measurements of higher-order moments. This leads us to introduce the concept of conditional spin-squeezing parameters, which quantify the metrological advantage provided by conditional states, as well as detect the presence of an EPR paradox.
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Karuseichyk, I., Sorelli, G., Walschaers, M., Treps, N., & Gessner, M. (2022). Resolving mutually-coherent point sources of light with arbitrary statistics. Phys. Rev. Res., 4(4), 043010–11pp.
Abstract: We analyze the problem of resolving two mutually coherent point sources with arbitrary quantum statistics, mutual phase, and relative and absolute intensity. We use a sensitivity measure based on the method of moments and compare direct imaging with spatial-mode demultiplexing (SPADE), analytically proving advantage of the latter. We show that the moment-based sensitivity of SPADE saturates the quantum Fisher information for all known cases, even for non-Gaussian states of the sources.
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