基于部分信息和有限资源的量子功提取

中文摘要 AI 辅助

信息可转化为功，但在量子力学中，关于态的信息并非可自由获取：必须通过对有限数量副本的测量进行统计推断。我们通过引入部分信息与有限资源（PIFR）量子麦克斯韦妖，研究这种有限资源场景下的功提取。给定N个具有已知哈密顿量的相同态副本，该妖测量M个副本以估计态及相应的功熵幺正变换，随后将该变换应用于剩余的N-M个副本。该协议在信息获取、重构精度和热力学产额之间引入了权衡，因此，归一化至理想功熵基准的总提取功成为相关的性能指标。作为核心结果，我们推导了一个通用闭式权衡界，该界将功熵效率置于卡诺型上限1-M/N与由有限样本量子估计理论导出的重构精度控制的下限之间；优化副本分配可得M*∝N^(2/3)，且在保守最坏情况重构精度设定下，以N^(-1/3)的速率趋近于理想极限。通过考虑标准量子态层析，我们数值验证了最优资源分布的存在，该分布还取决于所考虑态的纯度。我们的结果表明，有限副本功提取是一个真正依赖于任务的推断问题，其中估计策略应仅通过热力学性能而非重构保真度来评判。

英文摘要

Information can be converted into work, but in quantum mechanics information about a state is not freely available: it must be inferred statistically from measurements on a finite number of copies. We study work extraction in this finite-resource setting by introducing a partial-information and finite-resources (PIFR) quantum Maxwell's demon. Given $N$ identical copies of a state with known Hamiltonian, the demon measures $M$ copies to estimate the state and the corresponding ergotropic unitary, which is then applied to the remaining $N-M$ copies. This protocol induces a trade-off between information acquisition, reconstruction accuracy, and thermodynamic yield, making the total extracted work normalized to the ideal ergotropic benchmark the relevant figure of merit. As our central result, we derive a universal closed-form trade-off bound that places this ergotropic efficiency between a Carnot-type ceiling $1-M/N$ and a floor controlled by a reconstruction precision rooted in finite-sample quantum estimation theory; optimizing the copy allocation yields $M^*\propto N^{2/3}$ and an $N^{-1/3}$ approach to the ideal limit, set by a conservative, worst-case reconstruction precision. By considering standard quantum state tomography, we numerically verify the presence of an optimal resource distribution, which also depends on the purity of the state under consideration. Our results identify finite-copy work extraction as a genuinely task-dependent inference problem, in which estimation strategies should be judged by thermodynamic performance rather than reconstruction fidelity alone.

发表机构

• University of Pavia（帕维亚大学）
• INFN Sezione di Pavia（意大利国家核物理研究所帕维亚分部）

机构由 AI 辅助整理，请以论文原文为准。

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6 + 9 pages; 3 figures