标题： 被动态上的偏序关系与量子热力学中的霍夫曼优势关系 显示英文标题

标题： Partial order on passive states and Hoffman majorization in quantum thermodynamics

摘要： 被动态，即那些不能通过单位操作提取功的状态，在量子热力学的基础和应用中起着重要作用。 它们推广了熟悉的吉布斯热态，这些是唯一在张量积下稳定的被动态。 在这里，我们引入了一个被动态集合上的偏序关系，该关系捕捉了被动态比另一个被动态更“虚拟”冷的概念。 这个偏序关系，我们通过定义相对被动性的概念来构建，基于虚拟温度对被动态进行细粒度比较（就像热态根据其温度进行比较一样）。 然后，我们表征了在某些固定的输入和输出被动态下，对虚拟更冷状态集闭合的量子操作。 将状态的活性（即非被动性）视为一种资源，我们的主要结果是关于这些相对被动性保持操作下一类纯活性态变换的必要且充分条件。 该条件赋予了霍夫曼提出的非递增向量集合上的优超关系以量子热力学意义。 然后表明，在相对被动性保持操作下的最大可提取功等于这些纯活性态的熵力。 最后，我们能够完全表征量子比特系统中更简单情况下的保持被动性的操作，从而得出在保持被动性的量子比特操作下的状态转换条件。 这项工作的前景是超越热力学操作的量子操作中可提取功的通用资源理论框架。 显示英文摘要

摘要： Passive states, i.e., those states from which no work can be extracted via unitary operations, play an important role in the foundations and applications of quantum thermodynamics. They generalize the familiar Gibbs thermal states, which are the sole passive states being stable under tensor product. Here, we introduce a partial order on the set of passive states that captures the idea of a passive state being virtually cooler than another one. This partial order, which we build by defining the notion of relative passivity, offers a fine-grained comparison between passive states based on virtual temperatures (just like thermal states are compared based on their temperatures). We then characterize the quantum operations that are closed on the set of virtually cooler states with respect to some fixed input and output passive states. Viewing the activity, i.e., non-passivity, of a state as a resource, our main result is then a necessary and sufficient condition on the transformation of a class of pure active states under these relative passivity-preserving operations. This condition gives a quantum thermodynamical meaning to the majorization relation on the set of non-increasing vectors due to Hoffman. The maximum extractable work under relative passivity-preserving operations is then shown to be equal to the ergotropy of these pure active states. Finally, we are able to fully characterize passivity-preserving operations in the simpler case of qubit systems, and hence to derive a state interconversion condition under passivity-preserving qubit operations. The prospect of this work is a general resource-theoretical framework for the extractable work via quantum operations going beyond thermal operations.