Operational definition of a quantum speed limit
Operational definition of a quantum speed limit
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量子速度限制的操作定义
DOI：
10.1103/physrevresearch.2.023299
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发表时间：
2020
影响因子：
4.2
通讯作者：
Jing Liu
中科院分区：
文献类型：
--
作者：
Yanyan Shao;Bo Liu;Mao Zhang;Haidong Yuan;Jing Liu
量子速度极限是量子力学中的一个基本概念，其目的是寻找某些固定目标的最小时间尺度或最大动力学速度。在这一领域的大量研究中，构造演化时间的有效界一直是核心使命，但忽略了其背后的物理机制，以及哪些状态能够真正满足目标等基本问题。理解边界背后的物理原理至少和构建可达到的边界一样重要。在这里，我们提供了一个操作的方法来定义量子速度限制，它利用一组状态，可以满足目标来定义速度限制。它在各种情况下的性能进行了研究。对于与时间无关的哈密顿量，它与最高和最低能量之间的差成反比。它的可达性不需要零基态能量的事实表明它可以用作量子相变的指标。对于含时的哈密顿量，它表明，与现有的界限给出的结果相反，真正的速度限制应该是独立的时间。此外，在自发辐射的情况下，我们发现了一个违反直觉的现象，即糟糕的纯度有利于降低量子速度极限。
The quantum speed limit is a fundamental concept in quantum mechanics, which aims at finding the minimum time scale or the maximum dynamical speed for some fixed targets. In a large number of studies in this field, the construction of valid bounds for the evolution time is always the core mission, yet the physics behind it and some fundamental questions like which states can really fulfill the target are ignored. Understanding the physics behind the bounds is at least as important as constructing attainable bounds. Here we provide an operational approach for the definition of the quantum speed limit, which utilizes the set of states that can fulfill the target to define the speed limit. Its performances in various scenarios have been investigated. For time-independent Hamiltonians, it is inverse proportional to the difference between the highest and lowest energies. The fact that its attainability does not require a zero ground-state energy suggests it can be used as an indicator of quantum phase transitions. For time-dependent Hamiltonians, it is shown that, contrary to the results given by existing bounds, the true speed limit should be independent of the time. Moreover, in the case of spontaneous emission, we find a counterintuitive phenomenon that a lousy purity can benefit the reduction of the quantum speed limit.