论文标题
量子力学本体论模型中的经验上等效分布
Empirically Equivalent Distributions in Ontological Models of Quantum Mechanics
论文作者
论文摘要
我们考虑量子系统的本体论模型，假设不是空间上的所有概率分布$λ$的Ontic状态都是准备的，只有那些属于特定集合的概率分布。我们进一步假设每个具有有限值空间的POVM都可以测量，并且对于每个密度矩阵的每个密度矩阵都均为C分布在其成果统计中由密度矩阵给出了C的分布。我们表明，从C到密度矩阵集的映射必须是多对一的，也就是说，必须在C中进行经验上无法区分的分布。这表明，在自然界中，知识必须存在局限性，而这些事实是无法经验发现的。
We consider ontological models of a quantum system, assuming that not all probability distributions over the space $Λ$ of ontic states are preparable, only those belonging to a certain set C. We assume further that every POVM with a finite value space can be measured and that for every density matrix there exists a distribution in C whose outcome statistics is given by the density matrix. We show that this mapping from C to the set of density matrices must be many-to-one, that is, that there must be empirically indistinguishable distributions in C. This shows that there must be limitations to knowledge in the sense of facts in nature that cannot be discovered empirically.
