发表机构
Brown University; University of Iowa; University of Massachusetts Boston（布朗大学; 爱荷华大学; 马萨诸塞大学波士顿分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本论文从第一性原理推导QBism的非经典相干条件，证明其与广义概率理论等价，重构量子理论并提出与理论无关的复射影t-设计自检验方法。
AI 中文摘要
QBism（量子贝叶斯主义）将量子力学理解为概率论辅以额外的非经典相干条件。在本论文中，我们从第一性原理出发推导这些非经典相干条件，强调恰当选择参考测量的作用。在以主观贝叶斯方法处理标准概率后，我们证明QBist方法与现有广义概率理论框架等价。我们表明，基本非经典相干关系几乎总能被视为全概率定律的温和修正，并对实验场景何时具有经典解释给出融贯论说明。最后，我们证明当参考测量对应复射影3-设计时，量子态空间的形状隐含于表征该参考测量本身的概率中。因此，恰当理解下与这一单参考测量的相干性，意味着与所有有限维量子力学的相干性。我们随后尝试沿此思路对量子理论进行适度重构，其实践后果之一是一种与理论无关的、用于自检验t≥3的复射影t-设计的方法。
英文摘要
QBism understands quantum mechanics to be probability theory supplemented by additional nonclassical coherence conditions. In this dissertation, we develop these nonclassical coherence conditions from first principles, emphasizing the role of a well chosen reference measurement. After treating standard probability on subjective Bayesian lines, we demonstrate an equivalence between the QBist approach and the existing framework of generalized probabilistic theories. We show that the fundamental nonclassical coherence relation may almost always be taken to be a gentle modification of the law of total probability, and give a coherentist account of when an experimental scenario has a classical explanation. Finally, we show that when the reference measurement is chosen to correspond to a complex projective 3-design, the shape of quantum state space is implicit in the probabilities which characterize the reference measurement itself. Thus coherence with this single reference measurement, properly understood, implies coherence with all of finite dimensional quantum mechanics. We then attempt a modest reconstruction of quantum theory along these lines, one practical consequence of which is a method for self-testing complex projective $t$-designs for $t\ge 3$ in a theory-agnostic way.
Comments233 pages. 1 figure
