博恩的规则来自上下文相对缩最小化
1College of Engineering, University of Connecticut, Unit 3037, 261 Glenbrook Rd., Storrs, CT 06269, USA.
Entropy (Basel, Switzerland)
|September 27, 2025
概括
这项研究从测量环境中推导出量子概率,而不是作为假设. 它使用信息几何学量化上下文性,统一量子概率和经典结构.
科学领域:
- 量子信息理论 量子信息理论
- 量子力学的基础 量子力学的基础
- 数学物理 数学物理
背景情况:
- 波恩定律是量子力学的基础,它为测量结果提供了概率.
- 现有的方法通常假设Born规则或依赖复杂的框架.
- 了解量子概率的起源和上下文依赖性至关重要.
研究的目的:
- 为了提供波恩规则的变异性表征.
- 使用信息几何原理量化量子上下文性.
- 通过优化统一量子概率,上下文性和经典结构.
主要方法:
- 通过最小化Umegaki相对来对阿贝尔代数投射量子状态.
- 使用Petz的毕达哥拉斯的身份来导出Born的重量.
- 通过古典的Kullback-Leibler距离测量语境性到一个非语境的多类型.
- 采用束理论和分类结构.
主要成果:
- 出生的体重是由于最小化相对而得出的,而不是假设的.
- 一个凸的目标函数 Φ(ρ) 量化了上下文性,对于非上下文理论等于零.
- 最接近的非上下文模型被认为是经典的I投影.
- 该框架扩展到各种量子测量形式 (PVM,POVM).
结论:
- 这项工作提供了一个新的,信息几何衍生波恩规则.
- 它明确地解决和量化量子上下文性和概率的关系性质.
- 该方法将不同的概念统一为量子基础的单一优化原则.
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