arXiv 2108.042612021-08-09quant-phcond-mat.stat-mech

统一可观测量的量子和经典速度极限

Unifying Quantum and Classical Speed Limits on Observables

Luis Pedro García-Pintos, Schuyler Nicholson, Jason R. Green, Adolfo del Campo, Alexey V. Gorshkov

备注：: 8 pages with 2 figures in the main text; 13 pages in the appendix
发表信息：: Phys. Rev. X 12, 011038 (2022)
DOI：: 10.1103/PhysRevX.12.011038

摘要：

噪声的存在或与环境的相互作用可以从根本上改变一个孤立的量子系统的可观测量的动态。我们导出了开放量子系统的可观测量演化速度的一个界。这个速度限制分为Mandalestam和Tamm最初的时间-能量不确定性关系和最近为经典系统推导的时间-信息不确定性关系，两者都推广到开放量子系统。通过隔离系统动力学的相干和不相干的贡献，我们得到的下限和上限的进化速度。我们证明，后者提供了更严格的限制速度的观测比以前已知的量子速度限制，和一个优选的基础\emph{speed operators}服务，以完全表征饱和的速度限制的观测。我们使用这种结构来约束非相干动力学对可观测演化的影响，并找到使可观测演化的最大相干加速的哈密顿量。

英文摘要：

The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit divides into Mandalestam and Tamm's original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, generalizing both to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds to the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits, and that a preferred basis of \emph{speed operators} serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.

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