熵约束集的超越性质：第二部分
Transcendental properties of entropy-constrained sets: Part II
AI总结：
研究熵约束集的超越结构，排除了经典和量子情况下熵量的半代数单次刻画。
摘要：
在本工作中，我们通过利用各种熵约束集的半代数性质，探讨了某些单字母公式不可能性的问题。重点研究了相对熵、互信息和瑞尼熵的水平集性质。我们分析了在上述熵量固定时的状态集的超越结构。我们的结果排除了经典和量子情况下，具有受限辅助系统的这些熵量的半代数单次刻画。
英文摘要：
In this work, we address the question of the impossibility of certain single-letter formulas by exploiting the semi-algebraic nature of various entropy-constrained sets. The focus lies on studying the properties of the level sets of relative entropy, mutual information, and Rényi entropies. We analyze the transcendental structure of the set of states in which one of the aforementioned entropy quantities is fixed. Our results rule out (semi)algebraic single-shot characterizations of these entropy measures with bounded ancilla for both the classical and quantum cases.
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。
