发表机构
EDHEC Quantum Institute, EDHEC Business School（EDHEC量子研究所，EDHEC商学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将量子力学重新表述为未解决不确定性理论，以复值测度理论构建框架，明确物理现实的预概率描述，使可加性等在潜在性层面保持线性形式，对测量等概念给出统一潜在性解释，经验上等同于标准量子力学。
AI 中文摘要
我们提出将量子力学重新表述为一种未解决不确定性的理论。该框架用复值测度理论的语言来构建，被视为普通概率论的预概率对应物。在此表述中，可加性、条件性、独立性、混合、转移核和时间可分性在潜在性层面保持自然的线性形式，而非经典概率层面的特征如干涉则源于非线性的玻恩映射。测量被描述为潜在性基于已实现信息的贝叶斯型条件作用，非选择性测量则是用条件分支的统计混合取代相干潜在性。混合态、退相干、复合系统、纠缠和贝尔型关联也都有统一的潜在性层面解释。所得表述在经验上等同于标准量子力学，但明确了通常隐含在希尔伯特空间形式主义中的物理现实的预概率描述。
英文摘要
We propose a reformulation of quantum mechanics as a theory of unresolved uncertainty. This theory of potentiality is formulated in the language of complex-valued measure theory, regarded as a pre-probabilistic counterpart of ordinary probability theory. In this formulation, additivity, conditioning, independence, mixtures, transition kernels, and temporal divisibility retain natural linear forms at the potentiality level, while non-classical probability-level features such as interference arise from the nonlinear Born map. Measurement is described as Bayesian-type conditioning of potentialities on actualized information, and non-selective measurement as the replacement of coherent potentiality by statistical mixtures of conditional potentiality branches. Mixed states, decoherence, composite systems, entanglement, and Bell-type correlations are also given a unified potentiality-level interpretation. The density matrix is interpreted as a coherence kernel whose off-diagonal blocks encode retained phase relations. For pure bipartite states, potentiality independence is shown to be equivalent to factorization of the Born distribution in every pair of local contexts. The resulting formulation is empirically equivalent to standard quantum mechanics, but it makes explicit a pre-probabilistic description of physical reality that is usually implicit in the Hilbert-space formalism.
Comments16 pages, no figures
