Quantum non-Gaussian states of photons and phonons are conclusive and direct witnesses of higher-than-quadratic nonlinearities in optical and mechanical processes. Moreover, they are proven resources for quantum sensing, communication and error correction with diverse continuous-variable systems. This review introduces theoretical analyses of nonclassical and quantum non-Gaussian states of photons and phonons. It recapitulates approaches used to derive operational criteria for photons tolerant to optical losses, their application in experiments and their nowadays extension to quantum non-Gaussian photon coincidences. It extends to a recent comparison of quantum non-Gaussianity, including robustness to thermal noise, and sensing capability for high-quality phononic Fock states of single trapped cooled ions. The review can stimulate further development in the criteria of quantum non-Gaussian states and experimental effort to prepare and detect such useful features, navigating the community to advanced quantum physics and technology.

光子和声子的量子非高斯态是光学和机械过程中高于二次非线性的决定性和直接见证。此外，它们是经过验证的资源，可用于各种连续变量系统的量子传感、通信和纠错。这篇综述介绍了光子和声子的非经典和量子非高斯态的理论分析。它概括了用于推导光子耐受光学损耗的操作标准的方法、它们在实验中的应用以及它们现在扩展到量子非高斯光子巧合的方法。它扩展到最近对量子非高斯性的比较，包括对热噪声的鲁棒性，以及对单个捕获的冷却离子的高质量声子 Fock 状态的传感能力。