AI 中文总结
探讨通用量子功提取中一阶通用性是否延伸到可靠性，证明在相干量子比特时间平移轨道上，与相位无关的保持吉布斯态协议的最坏逐点指数受限，通过建立恒等式和运用不等式证明，明确输入态知识对可靠性不可或缺。
AI 中文摘要
通用功提取表明，获得渐近自由能率无需输入态知识。我们探讨这种一阶通用性是否延伸到可靠性，即提取失败的指数衰减率。在工作 - 电池保真度公式中，我们证明，在相干量子比特时间平移轨道上，没有与相位无关的保持吉布斯态协议能在整个过程中保持态感知保持吉布斯态指数：在每个正目标率下，其最坏的逐点指数受相应态感知热操作值限制。证明首先在相位鲁棒保持吉布斯态提取和态感知热提取之间建立精确的有限块长恒等式。然后，一个三角雷米兹不等式通过排除最坏相位的指数局部化，将此极小极大恒等式提升为逐点定理。对于一个明确的相干量子比特族，已知相位保持吉布斯态提取无误差，而每个与相位无关的协议都有有限的最坏逐点指数。因此，输入态知识对于一阶功率可能无关紧要，但对于最优指数可靠性却是不可或缺的。
英文摘要
Universal work extraction shows that input-state knowledge is unnecessary to attain the asymptotic free-energy rate. We ask whether this first-order universality extends to reliability, the exponential decay rate of extraction failure. In the work-battery fidelity formulation, we prove that no phase-independent Gibbs-preserving protocol can retain the state-aware Gibbs-preserving exponent throughout a coherent qubit time-translation orbit: at every positive target rate, its worst pointwise exponent is bounded by the corresponding state-aware thermal-operation value. The proof first establishes an exact finite-blocklength identity between phase-robust Gibbs-preserving extraction and state-aware thermal extraction. A trigonometric Remez inequality then upgrades this minimax identity to a pointwise theorem by ruling out exponential localization of the worst phase. For an explicit coherent-qubit family, known-phase Gibbs-preserving extraction is error free, whereas every phase-independent protocol has a finite worst-pointwise exponent. Thus input-state knowledge can be irrelevant to the first-order work rate yet indispensable for optimal exponential reliability.
