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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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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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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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Linowski, T., Schlichtholz, K., Sorelli, G., Gessner, M., Walschaers, M., Treps, N., et al. (2023). Application range of crosstalk-affected spatial demultiplexing for resolving separations between unbalanced sources. New J. Phys., 25(10), 103050–13pp.
Abstract: Super resolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution better than direct imaging even in the presence of measurement crosstalk (Gessner et al 2020 Phys. Rev. Lett. 125 100501). In this work, we consider arbitrarily unbalanced sources and provide a systematic analysis of the impact of crosstalk on the resolution obtained from SPADE. As we dissect, in this generalized scenario, SPADE's effectiveness depends non-trivially on the strength of crosstalk, relative brightness and the separation between the sources. In particular, for any source imbalance, SPADE performs worse than ideal direct imaging in the asymptotic limit of vanishing source separations. Nonetheless, for realistic values of crosstalk strength, SPADE is still the superior method for several orders of magnitude of source separations.
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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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