Mechanical systems prepared in quantum non-Gaussian states constitute a new advanced class of phenomena breaking the laws of classical physics. Specifically, such mechanical states cannot be described as any mixture of the Gaussian states produced by operations described by Hamiltonians at most quadratic in position and momentum, such as phase rotations, squeezing operations and linear driving. Therefore, they form a class of resourceful states for quantum technological tasks such as metrology, sensing, simulation and computation. Quantum opto- and electromechanics are advanced platforms for quantum mechanical experiments with broad applications offering various methods for preparing such mechanical quantum non-Gaussian states. The suitability of these platforms as transducers additionally allows the integration of such mechanical states into a variety of other related platforms. Here, we summarise the current techniques for creating these states, emphasizing those that have had experimental success and looking to methods that show promise for future experiments. By collating these results, we expect to stimulate new ideas for non-Gaussian state preparation in these fields, resulting in the realisation of further experiments. Moreover, we provide concise and clear explanations of the milestones of research in the quantum non-Gaussianity of mechanical states and its implementation and verification in a laboratory setting.

在量子非高斯态下制备的机械系统构成了打破经典物理定律的一类新的高级现象。具体来说，这种机械状态不能被描述为由哈密顿量所描述的位置和动量至多二次的操作产生的高斯状态的任何混合，例如相旋转、挤压操作和线性驱动。因此，它们形成了一类用于计量、传感、模拟和计算等量子技术任务的资源丰富的状态。量子光和机电是量子力学实验的先进平台，具有广泛的应用，提供了制备此类机械量子非高斯态的各种方法。这些平台作为传感器的适用性还允许将这种机械状态集成到各种其他相关平台中。在这里，我们总结了当前创建这些状态的技术，强调那些已经取得实验成功的技术，并寻找对未来实验有希望的方法。通过整理这些结果，我们期望激发这些领域非高斯态制备的新思路，从而实现进一步的实验。此外，我们还对机械态量子非高斯性研究的里程碑及其在实验室环境中的实施和验证提供了简洁明了的解释。