Geometric quantum speed limits and short-time accessibility to unitary operations
Geometric quantum speed limits and short-time accessibility to unitary operations
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DOI：
10.1103/physreva.99.042116
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发表时间：
2019-01
影响因子：
2.9
通讯作者：
P. Poggi
中科院分区：
文献类型：
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作者：
P. Poggi
量子速度极限（QSL）的概念是指两个量子态只有在有限的时间（称为QSL时间）之后才能在动力学演化中完全区分的基本事实。一个不同但相关的概念是最小控制时间（MCT），它是状态被驱动（通过合适的、通常依赖于时间的控制场）到给定目标状态所需的最小演化时间。虽然QSL可以提供有关MCT的信息，但它通常对其施加很少的限制，因此对于控制目的是不实用的。在这项工作中，我们重新审视这个问题，首先提出了一个理论的几何QSL的酉变换，而不是国家，并讨论其影响和局限性。然后，我们提出了一个框架，用于绑定MCT实现超越QSL结果的幺正变换，并提供更有意义的信息，以了解在短时间内系统的控制动力学。
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.