论文标题
紧密不确定性关系的量子速度限制
Quantum Speed Limit From Tighter Uncertainty Relation
论文作者
论文摘要
量子速度限制提供了一个基本的界限，该量子系统可以在任何物理操作下的初始状态和最终状态之间发展速度。著名的Mandelstam-Tamm（MT）绑定已广泛研究了正在进行统一时间演变的各种量子系统。在这里，我们使用纯量子系统进行任意统一进化的纯量子系统证明了新的量子速度限制。我们还得出了混合量子状态的更严格的不确定性关系，然后从中得出了混合量子状态的新量子速度限制，从而使其还原为从更严格的不确定性关系中得出的纯量子状态。我们表明，MT结合是此处得出的更严格的量子速度极限的特殊情况。我们还表明，当在许多不同的基础向量集中进行优化时，可以改善该界限。我们说明了使用随机哈密顿人的示例来说明纯状态的更高速度限制，并表明新的量子速度限制优于MT结合。
The quantum speed limit provides a fundamental bound on how fast a quantum system can evolve between the initial and the final states under any physical operation. The celebrated Mandelstam-Tamm (MT) bound has been widely studied for various quantum systems undergoing unitary time evolution. Here, we prove a new quantum speed limit using the tighter uncertainty relations for pure quantum systems undergoing arbitrary unitary evolution. We also derive a tighter uncertainty relation for mixed quantum states and then derive a new quantum speed limit for mixed quantum states from it such that it reduces to that of the pure quantum states derived from tighter uncertainty relations. We show that the MT bound is a special case of the tighter quantum speed limit derived here. We also show that this bound can be improved when optimized over many different sets of basis vectors. We illustrate the tighter speed limit for pure states with examples using random Hamiltonians and show that the new quantum speed limit outperforms the MT bound.
