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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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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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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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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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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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