We argue that the notion of pure sate within Standard Quantum Mechanics is presently applied within the specialized literature in relation to two mutually inconsistent definitions. While the first (operational purity) provides a basis-dependent definition which makes reference to the certain prediction of measurement outcomes, the latter (trace-invariant purity) provides a purely abstract invariant definition which lacks operational content. In this work we derive a theorem which exposes the serious inconsistencies existent within these two incompatible definitions of purity.

中文翻译：

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反对量子理论中“纯粹国家”的暴政

我们认为，标准量子力学中的纯态这一概念目前在专业文献中针对两个相互矛盾的定义应用。虽然第一个（操作纯度）提供了一个依赖于基础的定义，该定义引用了对测量结果的某些预测，但是后一个（痕量不变纯度）则提供了一个缺乏操作内容的纯抽象不变性定义。在这项工作中，我们得出了一个定理，该定理揭示了这两种不相容的纯度定义中存在的严重矛盾。