论文标题
量子理论中总概率及其在Wigner的朋友场景中的应用定律
Law of Total Probability in Quantum Theory and Its Application in Wigner's Friend Scenario
论文作者
论文摘要
众所周知，总概率定律在量子理论中一般不存在。但是，基于扩展的Wigner的朋友场景，对量子理论中一些基本假设的最新论点表明，有必要阐明如何在量子理论中以及在其仍然存在的条件下如何制定总概率定律。在这项工作中，量子理论中条件概率的定义扩展到POVM测量。为不兼容的POVM操作员提出了分配两次有条件概率的规则，这导致了总概率法律的更通用和精确的表述。确定总概率法律的足够条件。应用此处开发的理论分析与扩展的Wigner的朋友情景相关的几个量子无关定理揭示了这些无关定理中的逻辑漏洞。由于将总概率定律的有效性理所当然而没有验证足够的条件而存在，因此存在漏洞。因此，这些无关定理的矛盾仅重新确认量子理论中总概率的定律的无效性，而不是使无需定理试图驳斥的物理陈述无效。
It is well-known that the law of total probability does not hold in general in quantum theory. However, the recent arguments on some of the fundamental assumptions in quantum theory based on the extended Wigner's Friend scenario show a need to clarify how the law of total probability should be formulated in quantum theory and under what conditions it still holds. In this work, the definition of conditional probability in quantum theory is extended to POVM measurements. Rule to assign two-time conditional probability is proposed for incompatible POVM operators, which leads to a more general and precise formulation of the law of total probability. Sufficient conditions under which the law of total probability holds are identified. Applying the theory developed here to analyze several quantum no-go theorems related to the extended Wigner's friend scenario reveals logical loopholes in these no-go theorems. The loopholes exist as a consequence of taking for granted the validity of the law of total probability without verifying the sufficient conditions. Consequently, the contradictions in these no-go theorems only reconfirm the invalidity of the law of total probability in quantum theory, rather than invalidating the physical statements that the no-go theorems attempt to refute.
