The study of feedback control inspired by Maxwell's demon is central to the understanding of the relationship between thermodynamics and information. In this paper, we establish fundamental lower limits on the work costs of system conversion with quantum feedback, where quantum side information acquired in advance can be fed back to the system coherently by a controller. From two basic operational principles that every physically admissible feedback-control scheme should satisfy, we derive the tightest possible bounds on the single-shot work of formation and extractable work of an arbitrary quantum system given arbitrary quantum side information held by the controller. These bounds are expressed in terms of information measures simultaneously generalizing conditional entropies, mutual informations, and relative entropies. In the asymptotic limit, they lead to a generalized second law of thermodynamics with quantum feedback, featuring a conditional Helmholtz free energy. Our findings also provide precise thermodynamic meanings for the negativity of single-shot conditional entropies and resolve an open problem in the axiomatic reconstruction of such conditional entropies.

翻译：受麦克斯韦妖启发的反馈控制研究，对于理解热力学与信息之间的关系至关重要。本文针对量子反馈下的系统转换过程，建立了其所需功的基本下限。在此过程中，控制器可以相干地将预先获取的量子侧信息反馈给系统。基于所有物理上可容许的反馈控制方案都应满足的两条基本操作原理，我们推导出了在控制器持有任意量子侧信息的条件下，任意量子系统的单次形成功与可提取功的最紧可能界限。这些界限以信息测度表示，这些测度同时推广了条件熵、互信息和相对熵。在渐近极限下，它们导出了一个包含量子反馈的广义热力学第二定律，其核心是一个条件亥姆霍兹自由能。我们的研究结果还为单次条件熵的负性提供了精确的热力学解释，并解决了此类条件熵公理化重构中的一个开放性问题。