Energetics of non-Gaussianity in single mode cavities
Non-Gaussian states are key resources for quantum technologies, making the quantification of non-Gaussianity a fundamental challenge. We introduce an energetic framework for characterizing non-Gaussianity in single-mode bosonic states by decomposing the total energy into Gaussian and non-Gaussian contributions. For pure states, we show that the non-Gaussian energy defines a bona fide measure of non-Gaussianity and establish a direct connection with the relative entropy of non- Gaussianity. As an illustration, we consider non-Gaussian states generated from coherent states with tunable amplitudes using a SNAP gate. We find that the resulting non-Gaussian energy and Wigner negativity are maximized at similar input amplitudes. For mixed states, we demonstrate that the non-Gaussian energy provides a faithful witness of non-Gaussianity. Our results uncover an energetic fine structure of non-Gaussian quantum states and offer new insights into the efficient generation and manipulation of non-Gaussian resources.