标题： 几何量子速度极限与对酉操作的短时间可达性 显示英文标题

标题： Geometric quantum speed limits and short-time accessibility to unitary operations

摘要： 量子速限（QSL）的概念指的是一个基本事实，即两个量子态只有在经过一段时间后才能完全区分，这段时间称为QSL时间。 另一个相关概念是最小控制时间（MCT），这是将一个状态通过适当的、通常为时变的控制场驱动到给定目标状态所需的最短演化时间。 虽然QSL可以提供关于MCT的信息，但它通常对MCT的限制很少，因此对于控制目的来说并不实际。 在本工作中，我们首先提出一种针对单位变换而非状态的几何QSL理论，并讨论其含义和局限性。 然后，我们提出一种用于界定实现单位变换的MCT的框架，该框架超越了QSL的结果，并提供了更有意义的信息来理解系统在短时间内受控动力学的行为。 显示英文摘要

摘要： The notion of quantum speed limit (QSL) refers to the fundamental fact that two quantum states become completely distinguishable upon dynamical evolution only after a finite amount time, called the QSL time. A different, but related concept is that of minimum control time (MCT), which is the minimum evolution time needed for a state to be driven (by suitable, generally time-dependent, control fields) to a given target state. While the QSL can give information about the MCT, it usually imposes little restrictions to it, and is thus unpractical for control purposes. In this work we revisit this issue by first presenting a theory of geometrical QSL for unitary transformations, rather than for states, and discuss its implications and limitations. Then, we propose a framework for bounding the MCT for realizing unitary transformations that goes beyond the QSL results and gives much more meaningful information to understand the controlled dynamics of the system at short times.