量子张量积的任何扩展都不承认叠加原理
No extension of the Quantum Tensor Product admits a Superposition principle
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中文总结 AI 辅助
该研究在广义概率理论框架内定义叠加，构建三条叠加原理，证明量子张量积是满足所有原理的量子系统最大复合规则，还将纠缠等非经典特征归为叠加的特殊形式。
中文摘要 AI 辅助
教科书上的量子叠加指的是，希尔伯特空间射线的某些线性组合（每条射线代表一个有效量子态）本身也是有效态。这一概念不具有可操作性，且依赖于底层的希尔伯特空间形式体系。近期针对不定因果序的实验测试以及探测引力非经典性的测试，均以叠加为核心，因此需要一种独立于量子理论、具有可操作性的该概念的形式化表述。本文在广义概率理论框架内，基于制备-测量实验中的观测统计数据定义叠加，据此构建三条叠加原理，以探究量子理论的哪些结构特征可推广至其他理论。我们研究这些原理能否从子系统推广至其复合系统的条件；为此，我们证明，量子张量积是满足所有三条原理的量子系统的最大复合规则。此外，我们还证明，纠缠和制备不确定性等非经典特征可被视为叠加的特殊形式。
英文摘要
Textbook quantum superposition refers to the feature that certain linear combinations of Hilbert space rays, each representing a valid quantum state, are themselves valid states. This notion is not operational, and it relies on the underlying Hilbert space formalism. Recent proposals for experimental tests of indefinite causal order, as well as tests probing the non-classicality of gravity, pivot on superposition, thereby calling for a theory-independent, operational formalisation of the concept. Here, we define superposition within the framework of Generalised Probabilistic Theories, based on observed statistics in prepare-and-measure experiments. Using this, we formulate three superposition principles to investigate which structural features of quantum theory carry over to other theories. We study conditions under which these principles carry over from subsystems to their compositions; to this end, we show that the quantum tensor product emerges as the largest composition rule for quantum systems respecting all three principles. Furthermore, we show how non-classical features such as entanglement and preparational uncertainty can be viewed as special forms of superposition.
