AI 中文总结
研究响应寄存器量子预言机中值读出与相位反冲的定量关系，证明有限阿贝尔响应群中最优单查询值读出概率是响应状态的归一化Rényi - ½有效傅里叶支撑，给出其信息论表征、操作解释及相关定理。
AI 中文摘要
响应寄存器量子预言机有值读出和相位反冲两种互补的操作解释。尽管它们的计算等效性已为人熟知，但这两种操作解释之间的定量关系缺乏精确表征。我们证明，对于有限阿贝尔响应群，最优单查询值读出概率恰好是响应状态的归一化Rényi - ½有效傅里叶支撑。此恒等式提供了最优值读出能力的精确信息论表征，赋予Rényi - ½有效傅里叶支撑在预言机设置中的直接操作解释，并产生了一个紧密的相位 - 值互补定理以及一族饱和响应状态。
英文摘要
Response-register quantum oracles admit two complementary operational interpretations: value readout and phase kickback. Although their computational equivalence is well understood, the quantitative relation between these two operational interpretations has lacked an exact characterization. We prove that, for finite Abelian response groups, the optimal single-query value-readout probability is exactly the normalized Rényi-1/2 effective Fourier support of the response state. This identity provides an exact information-theoretic characterization of optimal value-readout capability, gives the Rényi-1/2 effective Fourier support a direct operational interpretation in the oracle setting, and yields a tight phase--value complementarity theorem together with an explicit family of saturating response states.
Comments12 pages, 4 figures, Comments and suggestions are most welcome
