Our starting point was to research on possible formulations of experimentally accessible criteria for certifying and quantifying genuine quantum correlations. First, we proposed a method for the conditional generation of nonclassical states of light in a cavity [Phys. Rev. A 100, 043812 (2019)]. Nonclassical properties of the cavity mode, as quadrature squeezing, sub-Poissonian photon-number distributions, and negative Wigner function, are identified and characterized. Next, we derive a family of inequalities (based on Chebyshev's inequality) involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state [Phys. Rev. Lett. 124, 133601 (2020)]. The violation of these inequalities is a clear signature of nonclassicality. Our approach combines the characterization of nonclassical effects via negativities in phase-space distributions with inequality conditions usually being formulated for moments of physical observables. Importantly, the obtained criteria certify nonclassicality even when the involved phase-space distributions are non-negative. Following this lead, we look for the possibilities of generalization of such phase space inequalities. Thus, we devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions [Quantum 4, 343 (2020)]. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Once our method was proposed and generalized, we team up with experimentalists to certify experimentally nonclassicality via phase-space inequalities [Phys. Rev. Lett. 126, 023605 (2021)]. In addition, we implement a robust kind of nonclassical photon-photon correlated state, with quantum correlations beyond entanglement and quantum discord, with useful applications in quantum information processing. For this contribution, we team up with experimental and theory groups in Germany to certify the presence of such quantum correlations via negativities in the regularized two-mode Glauber-Sudarshan function [Phys. Rev. Lett. 126, 170404 (2021)] and also show how multimode entanglement can be activated based on the generated, nonentangled state.
We worked on the investigation of efficient techniques to either certify, store, transmit, extract or quantify quantum information from highly dimensional states, independently if they are DV or CV systems. We explored different aspects of characterization and measurements of quantum states and parameters. Firstly, we considered three paradigmatic estimation schemes in continuous-variable quantum metrology and analysed them from the Bayesian perspective [Quantum Sci. Technol. 6 025018 (2021)]. We identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Besides precision, the fast and accessible verification of nonclassical resources is an indispensable step towards a broad utilization of continuous-variable quantum technologies. We use machine learning methods for the identification of nonclassicality of quantum states of light by processing experimental data obtained via homodyne detection [Phys. Rev. Research 3, 023229 (2021)]. For this purpose, we train an artificial neural network to classify classical and nonclassical states from their quadrature-measurement distributions.
