The so-called stellar formalism allows us to represent the non-Gaussian properties of single-mode quantum states by the distribution of the zeros of their Husimi Q function in phase space. We use this representation in order to derive an infinite hierarchy of single-mode states based on the number of zeros of the Husimi Q function: the stellar hierarchy. We give an operational characterization of the states in this hierarchy with the minimal number of single-photon additions needed to engineer them, and derive equivalence classes under Gaussian unitary operations. We study in detail the topological properties of this hierarchy with respect to the trace norm, and discuss implications for non-Gaussian state engineering, and continuous variable quantum computing.

中文翻译：

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非高斯量子态的恒星表示。

所谓的恒星形式主义使我们能够通过相空间中Husimi Q函数的零点分布来表示单模量子态的非高斯性质。我们使用这种表示法来基于Husimi Q函数的零数目（恒星层次）来导出单模状态的无限层次。我们对这种状态下的状态进行了操作表征，并用最少的单光子加成来对它们进行工程化，并推导出高斯unit运算下的等价类。我们详细研究了有关跟踪规范的此层次结构的拓扑属性，并讨论了对非高斯状态工程和连续变量量子计算的影响。