AI 中文总结
研究被动高斯林德布拉德网络近似1/|ω|谱的问题，证明模式间耦合无法减少所需辅助模式数量，给出了规定容差下的最小模式数及规定模式预算下的最大动态范围。
AI 中文摘要
用有限数量的马尔可夫辅助模式表示连续环境是非马尔可夫开放量子系统的基础，但一个关键问题仍未解决：在固定模式预算下，模式间的相干耦合能否减少谱近似误差？我们证明，当具有守恒粒子数的被动高斯林德布拉德辅助网络在有限双边频率带上近似1/|ω|谱时，模式间耦合并无优势。对于任意模式预算N，一般耦合类与其无耦合对角子类具有相同的最优误差，该误差恰好是符号近似的2N阶佐洛塔廖夫误差。此最优值可由N个零失谐的独立阻尼辅助模式实现。该结果成立的条件为：辅助网络处于定态真空态，系统通过单个厄米算符与该网络耦合，且无白噪声直通项。因此，尽管一般耦合网络具有O(N²)个实参数，但模式间的相干耦合、集体耗散及非正规结构无法减少达到规定容差所需的辅助模式数量。这一精确关系既给出了规定正频率动态范围和容差下的最小模式数量，也给出了规定模式预算和容差下可达到的最大动态范围。
英文摘要
Representing continuous environments by finitely many Markovian auxiliary modes is fundamental in non-Markovian open quantum systems, yet a critical question remains: at a fixed mode budget, can coherent intermode coupling reduce the spectral approximation error? We prove that intermode coupling offers no advantage when passive, number-conserving Gaussian Lindblad auxiliary networks approximate a $1/|ω|$ spectrum over a finite two-sided frequency band. For any mode budget $N$, the general coupled class and its uncoupled diagonal subclass share the same optimal error, which is exactly the degree-$2N$ Zolotarev error for sign approximation. This optimum is attainable by $N$ independent damped auxiliary modes at zero detuning. The result holds when the auxiliary network is in a stationary vacuum state, the system couples to it via a single Hermitian bath operator, and no white-noise feedthrough term is present. Consequently, although a general coupled network has $O(N^{2})$ real parameters, coherent intermode coupling, collective dissipation, and nonnormal structure cannot reduce the number of auxiliary modes required to reach a prescribed tolerance. This exact relation yields both the minimum mode count for a prescribed positive-frequency dynamic range and tolerance, and the maximum dynamic range attainable for a prescribed mode budget and tolerance.
