--- _id: '26290' abstract: - lang: eng text: 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. Our approach complements and extends recent results that were based on Chebyshev's integral inequality \cite{BA19}. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyond s-parametrized ones, and is accessible in experiments. 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. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions. article_number: '343' author: - first_name: Martin full_name: Bohmann, Martin last_name: Bohmann - first_name: Elizabeth full_name: Agudelo, Elizabeth last_name: Agudelo - first_name: Jan full_name: Sperling, Jan id: '75127' last_name: Sperling orcid: 0000-0002-5844-3205 citation: ama: Bohmann M, Agudelo E, Sperling J. Probing nonclassicality with matrices of phase-space distributions. Quantum. Published online 2020. doi:10.22331/q-2020-10-15-343 apa: Bohmann, M., Agudelo, E., & Sperling, J. (2020). Probing nonclassicality with matrices of phase-space distributions. Quantum, Article 343. https://doi.org/10.22331/q-2020-10-15-343 bibtex: '@article{Bohmann_Agudelo_Sperling_2020, title={Probing nonclassicality with matrices of phase-space distributions}, DOI={10.22331/q-2020-10-15-343}, number={343}, journal={Quantum}, author={Bohmann, Martin and Agudelo, Elizabeth and Sperling, Jan}, year={2020} }' chicago: Bohmann, Martin, Elizabeth Agudelo, and Jan Sperling. “Probing Nonclassicality with Matrices of Phase-Space Distributions.” Quantum, 2020. https://doi.org/10.22331/q-2020-10-15-343. ieee: 'M. Bohmann, E. Agudelo, and J. Sperling, “Probing nonclassicality with matrices of phase-space distributions,” Quantum, Art. no. 343, 2020, doi: 10.22331/q-2020-10-15-343.' mla: Bohmann, Martin, et al. “Probing Nonclassicality with Matrices of Phase-Space Distributions.” Quantum, 343, 2020, doi:10.22331/q-2020-10-15-343. short: M. Bohmann, E. Agudelo, J. Sperling, Quantum (2020). date_created: 2021-10-15T16:10:46Z date_updated: 2023-04-20T15:12:58Z department: - _id: '15' - _id: '170' - _id: '706' - _id: '35' doi: 10.22331/q-2020-10-15-343 language: - iso: eng publication: Quantum publication_identifier: issn: - 2521-327X publication_status: published status: public title: Probing nonclassicality with matrices of phase-space distributions type: journal_article user_id: '16199' year: '2020' ...