AI 中文总结
研究宽带量子存储器接口评估问题，通过正实频谱导纳建模无源多谐振器接口，证明有限无源有理接口反射特性及相关下限，给出精确计算机辅助证书，如11模式设计的反射边界及写入保证，提供指定接口可重复证书。
AI 中文摘要
宽带量子存储器接口通常通过中心频率阻抗匹配或采样效率曲线进行评估。但两者都无法提供连续带操作证书，且吸收并非自动可逆存储。我们通过具有明确识别的受控输出通道的正实频谱导纳对无源单端口多谐振器接口进行建模。若其一光子子空间等距映射到长寿命寄存器，对于在频带\(\mathcal{B}\)中支持的归一化频谱\(f\)，写入概率为\(1-\int_{\mathcal{B}} |r(i\omega)|^2 |f(\omega)|^2\,d\omega\)，最坏情况写入效率为\(1-\|r\|_{L^\infty(\mathcal{B})}^2\)。我们证明了有限无源有理接口在非零区间上不能有零反射，并推导出半宽度为\(B\)的频带的博德 - 法诺下限\(\|r\|_\infty \geq \exp[-\pi\kappa/(2B)]\)。在固定极点位置，极小极大合成是振荡器强度中的拟凸半无限问题。然后我们给出精确的计算机辅助证书：在十进制设计转换为显式有理系统后，连续反射边界变为一个单变量多项式的正性，并通过斯图姆根计数证明；精确的劳斯 - 赫尔维茨行列式证明稳定性和最小相位。在\(\kappa = 2\)和\(B = 1\)的单位下，一个11模式设计满足\(0.064112405 \leq \|r\|_\infty < 0.0641125\)，这意味着有条件的均匀写入保证高于\(0.995889587\)。这是指定接口的可重复证书，而非全局可移动极点最优性或实验完整存储器的声明。
英文摘要
Broadband quantum-memory interfaces are often assessed by center-frequency impedance matching or by a sampled efficiency curve. Neither supplies an operational continuous-band certificate, and absorption is not automatically reversible storage. We model a passive one-port multiresonator interface by a positive-real spectral admittance with explicitly identified controlled output channels. If their one-photon subspace is mapped isometrically into long-lived registers, the write probability for a normalized spectrum $f$ supported in a band $\mathcal{B}$ is $1-\int_{\mathcal{B}} |r(iω)|^2 |f(ω)|^2\,dω$, and the worst-case write efficiency is $1-\|r\|_{L^\infty(\mathcal{B})}^2$. We prove that a finite passive rational interface cannot have zero reflection on a nonzero interval and derive the Bode--Fano floor $\|r\|_\infty \geq \exp[-πκ/(2B)]$ for a band of half-width $B$. At fixed pole locations, minimax synthesis is a quasiconvex semi-infinite problem in the oscillator strengths. We then give an exact computer-assisted certificate: after a decimal design is converted into an explicit rational system, the continuum reflection bound becomes positivity of one univariate polynomial and is proved by Sturm root counting; exact Routh--Hurwitz determinants certify stability and minimum phase. In units $κ=2$ and $B=1$, an 11-mode design obeys $0.064112405 \leq \|r\|_\infty < 0.0641125$, implying a conditional uniform write guarantee above $0.995889587$. This is a reproducible certificate for a specified interface, not a claim of global movable-pole optimality or of an experimentally complete memory.
Comments11 pages, 4 figures. Includes exact computer-assisted continuum certificates based on Sturm root counting and Routh--Hurwitz determinants
