While the sensitivity limits for classical and quantum strategies are well known for the estimation of a single parameter, this is less clear in the multiparameter case. We study sensitivity bounds for an ensemble of parameters in quantum metrology. We further aim to understand the potential of particle- and mode entanglement for applications in multiparameter quantum metrology.

• M. Gessner, A. Smerzi, and L. Pezzè, Nat. Commun. 11, 3817 (2020).

• M. Gessner, L. Pezzè, and A. Smerzi, Phys. Rev. Lett. 121, 130503 (2018).

Squeezing is the leading strategy to achieve a quantum enhancement in practice. The sensitivity of Gaussian quantum states is effectively described in terms of reduced (squeezed) variances for linear observables, such as collective spin operators (spin squeezing). Non-Gaussian states can have very sensitive features with an even higher metrological potential. The characterization of these states poses a significant challenge for theory and experiment.

We develop methods for characterization of non-Gaussian quantum states in both discrete- and continuous-variable systems, e.g., by generalizing the concept of spin squeezing to nonlinear observables. One approach is to identify the optimal measurement observables for arbitrary quantum states that yield the highest sensitivity in phase estimation.

• Y. Baamara, A. Sinatra, M. Gessner, Phys. Rev. Lett. 127, 160501(2021); Comptes Rendus. Physique 23, 1 (2022).

• M. Gessner, A. Smerzi, L. Pezzè, Phys. Rev. Lett. 122, 090503 (2019).

• F. Wolf et al., Nat. Commun. 10, 2929 (2019).

The resolution of imaging devices that collect the light’s intensity distribution (e.g. CCD cameras) is limited by Rayleigh’s criterion (i.e. roughly half the wavelength of the emitted light). Other measurements, such as spatial mode decompositions, are able to overcome this limit. We use tools from the theory of quantum parameter estimation to systematically optimize the quantum measurement in the imaging plane, to develop experimentally realistic superresolution methods, and to identify their limits.

• G. Sorelli, M. Gessner, M. Walschaers, N. Treps, Phys. Rev. Lett. 127, 123604 (2021); Phys. Rev. A 104, 033515 (2021).

• M. Gessner, C. Fabre, N. Treps, Phys. Rev. Lett. 125, 100501 (2020).

• M. Gessner, N. Treps, and C. Fabre, Optica 10, 996 (2023).

The well-known Cramér-Rao bound defines the sensitivity limit for the estimation of a fixed parameter for a frequentist interpretation of probability and becomes relevant usually only after many repeated measurements. Other interesting scenarios emerge by taking on a Bayesian point-of-view, in the presence of finite signal-to-noise ratio, or when estimating fluctuating parameters. We are interested in the identification of suitable bounds for such non-standard scenarios and to compare their performance with simulated quantum estimation experiments.

The sensitivity of quantum states is closely related to their statistical speed under a phase-imprinting evolution: The faster a state evolves under the variation of a parameter, the higher its potential to yield a precise estimate of the parameter. We study different notions of quantum statistical speed and their relation to sensitivity and entanglement.

• M. Gessner and A. Smerzi, Phys. Rev. Lett. 130, 260801 (2023).

• Y. Li et al., Entropy 20, 628 (2018).

• M. Gessner and A. Smerzi, Phys. Rev. A 97, 022109 (2018).