在两个随机数生成问题中,使用平滑的雷尼 entropy 的f-divergences 的最佳可实现率
1Center for Data Science, Waseda University, Tokyo 169-8050, Japan.
Entropy (Basel, Switzerland)
|September 27, 2024
概括
本研究分析了使用光滑的雷尼对f-分歧的随机数生成率. 它揭示了源解析性和内在随机性之间的二元性,扩展了之前的发现.
科学领域:
- 信息理论 信息理论
- 可能性理论概率理论.
- 随机数生成器 随机数生成器
背景情况:
- 对于一般源来说,随机数生成的两个关键问题是源的可解析性和内在的随机性.
- 最佳可实现的速率通常以信息频谱和光滑的雷尼 Entropy为特征.
- 最近的工作使用信息频谱来描述f-分歧的速率,但光滑的雷尼 entropi仍然未被探索.
研究的目的:
- 分析使用平滑的雷尼 Entropy 对 f-Divergence 的随机数生成问题的最佳可实现率.
- 扩大在这些问题中考虑的f-分歧类.
- 调查一级和二级利率,以及乐观的可实现利率.
主要方法:
- 关于f-差异的第一阶段最佳可实现率的一般公式的推导.
- 在f-分歧上放松条件以概括公式.
- 将一般公式细分化为特定函数 f.
主要成果:
- 关于f-差异的第一阶段最佳可实现率的一般公式得到.
- 由f-分歧的放松条件对衍生式进行概括.
- 可解决性和内在随机性之间的二元性在光滑的雷尼 Entropy 中被揭示出来.
结论:
- 该研究提供了一个统一的框架,用于分析使用光滑的雷尼和f-分歧的随机数生成率.
- 这些发现扩展了现有的结果,并提供了关于源可解决性和内在随机性之间的关系的新见解.
- 衍生出的一般公式简化了对各种重要措施的最佳可实现率的计算.
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