允许平均变距为正值的变长内在随机性
Variable-Length Intrinsic Randomness Allowing Positive Value of the Average Variational Distance
摘要：
本文考虑变长内在随机性问题。我们提出的平均变距离作为性能标准的角度来看，一个对偶关系的问题制定可变长度的可解性。以前的研究已经导出了$ε$ -变长可分辨性的一般公式。推导了变长内禀随机性$ε$的一般公式。即在平均变分距离小于或等于一个常数$ε$的约束下，刻画了平均长度的上确界.我们的结果阐明了$ε$ -变长可分辨性和$ε$ -变长内禀随机性的一般公式之间的对偶关系。我们还推导出表征我们的一般公式的量的下界。
英文摘要：
This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the $ε$-variable-length resolvability. We derive the general formula of the $ε$-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint that the value of the average variational distance is smaller than or equal to a constant $ε$. Our result clarifies a dual relationship between the general formula of $ε$-variable-length resolvability and that of $ε$-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
