Nonclassical kernels in continuous-variable systems

Kernel methods are ubiquitous in classical machine learning, and recently their formal similarity with quantum mechanics has been established. To grasp the potential advantage of quantum machine learning, it is necessary to understand the distinction between nonclassical kernel functions and classical kernels. This paper builds on a recently proposed phase-space nonclassicality witness [Bohmann and Agudelo, Phys. Rev. Lett. 124, 133601 (2020)] to derive a witness for the kernel's quantumness in continuous-variable systems. We discuss the role of the kernel's nonclassicality in data distribution in the feature space and the effect of imperfect state preparation. Furthermore, we show that the nonclassical kernels lead to the quantum advantage in parameter estimation. Our work highlights the role of the phase-space correlation functions in understanding the distinction of classical machine learning from quantum machine learning.