论文标题
哪些浴室 - 哈米尔顿人对热作战很重要？
Which Bath-Hamiltonians Matter for Thermal Operations?
论文作者
论文摘要
在本文中，我们从数学和拓扑的角度探索了一组热作战。首先，我们介绍了有关某些参考汉密尔顿人的谐音谱的概念，然后证明，在定义热行动时，只能考虑仅考虑满足这种共振特性的浴室。接下来，我们将在某些参数（例如系统的能量和浴室的温度）中研究一组热作战的连续性。我们将看到，在任何具有所谓的退化Bohr Spectrum的Hausdorff度量的Hausdorff度量方面，一组热作战都不断变化，无论温度如何。最后，我们通过通过三个实际参数表征任何此类操作，从而在二维中找到了（增强的）热作战的半群表示，从而可以可视化该集合。使用此情况，在Qubit案例中，我们显示了（增强的）热作战的通勤性以及没有闭合的热作战的凸度。后者是通过准确指定该集合的元素来完成的。
In this article we explore the set of thermal operations from a mathematical and topological point of view. First we introduce the concept of Hamiltonians with resonant spectrum with respect to some reference Hamiltonian, followed by proving that when defining thermal operations it suffices to only consider bath Hamiltonians which satisfy this resonance property. Next we investigate continuity of the set of thermal operations in certain parameters, such as energies of the system and temperature of the bath. We will see that the set of thermal operations changes discontinuously with respect to the Hausdorff metric at any Hamiltonian which has so-called degenerate Bohr spectrum, regardless of the temperature. Finally we find a semigroup representation of the (enhanced) thermal operations in two dimensions by characterizing any such operation via three real parameters, thus allowing for a visualization of this set. Using this, in the qubit case we show commutativity of the (enhanced) thermal operations as well as convexity of the thermal operations without the closure. The latter is done by specifying the elements of this set exactly.
