AI 中文总结
该研究针对随机测量下的 daemon 功，证明两量子比特纠缠纯态可实现无涨落的最大增益，确立随机 daemon 功为纠缠的热力学探针，揭示测量诱导功涨落与关联类型的联系。
AI 中文摘要
优化后的 daemon 功可使纠缠在测量辅助的功提取中失去热力学必要性：对于固定的系统边际，量子-经典态可通过优化辅助测量重现辅助测量所能获得的最大功。我们证明，当辅助测量为随机测量时，这种等价性被打破。对于在 Haar 随机投影测量下的 qudit-qubit 量子-经典态，我们推导了平均 daemon 增益的上界，并证明了增益-涨落权衡关系，表明任何正的随机增益必然伴随测量诱导的涨落。与之形成鲜明对比的是，一类两量子比特纠缠纯态达到了系统边际允许的增益代数最大值，同时对每个测量基矢保持无涨落，产生的增益至少是具有相同边际的任何量子-经典态所能达到的两倍。我们进一步证明，当考虑一般两量子比特可分态时，上述结论成立，将随机增益定位为纠缠认证的充分判据。最后，我们表明，当从最优基矢周围的极冠区域采样的部分随机测量下，纠缠优势仍然存在。这些结果确立了随机 daemon 功作为纠缠的热力学探针，并揭示了测量诱导的功涨落与关联类型（量子纠缠 vs 经典关联）之间的联系。
英文摘要
Optimized daemonic ergotropy can make entanglement thermodynamically dispensable in measurement-assisted work extraction: for a fixed system marginal, quantum-classical states can reproduce the maximal work obtainable by optimizing the auxiliary measurement. We show that this equivalence is broken when the auxiliary measurement is randomized. For qudit-qubit quantum-classical states under Haar-random projective measurements, we derive upper bounds on the averaged daemonic gain and prove a gain-fluctuation trade-off, showing that any positive randomized gain necessarily entails measurement-induced fluctuations. In sharp contrast, a family of two-qubit entangled pure states attains the algebraic maximum of the gain allowed by a system marginal while remaining fluctuation-free for every measurement basis, yielding at least twice the gain achievable by any quantum-classical state with the same marginal. We further demonstrate that such conclusion holds when general two-qubit separable states are considered positioning randomized gain as a sufficient criterion for entanglement certification. Finally, we show that the entanglement advantage persists under partially randomized measurements sampled from a polar cap around the optimal basis. These results establish randomized daemonic ergotropy as a thermodynamic probe of entanglement and exhibit the connection between measurement-induced work fluctuations on the type of correlations: quantum entanglement vs classical.
Comments7+10 pages, 2 figures
