反驳量子速度极限假设的封闭系统
Closed systems refuting quantum-speed-limit hypotheses
AI总结：
该研究通过理论推导反驳了Margolus-Levitin量子速度极限可推广至封闭系统的普遍观点，同时证明孤立系统中Mandelstam-Tamm与Bhatia-Davies量子速度极限同步饱和，且存在仅饱和前者的封闭系统。
摘要：
许多针对孤立系统的量子速度极限可推广至也适用于封闭系统，例如著名的Mandelstam-Tamm（曼德尔斯坦-塔姆）量子速度极限便是如此。Margolus和列维京（Levitin）推导出了同样知名且表面上相关的量子速度极限，且人们似乎普遍认为Margolus-Levitin量子速度极限也能类似地推广到封闭系统。然而，近期对该极限的几何分析显示，它与大多数已知的量子速度极限存在显著差异。本文中我们证明，与普遍观点相反，Margolus-Levitin量子速度极限无法以显而易见的方式推广到封闭系统。更确切地说，我们表明对于每一个Margolus-Levitin型的假设界，都存在这样的封闭系统：其在具有任意给定保真度的态之间演化时，保持归一化期望能量守恒，且演化时间短于该界值。我们还证明，对于孤立系统，Mandelstam-Tamm量子速度极限以及我们称之为Bhatia-Davies（巴蒂亚-戴维斯）量子速度极限的该极限的稍弱版本始终同时达到饱和。这两种演化时间估计都能直接推广到封闭系统。我们证实存在这样的封闭系统：其能达到Mandelstam-Tamm量子速度极限的饱和，但无法达到Bhatia-Davies量子速度极限的饱和。
英文摘要：
Many quantum speed limits for isolated systems can be generalized to also apply to closed systems. This is, for example, the case with the well-known Mandelstam-Tamm quantum speed limit. Margolus and Levitin derived an equally well-known and ostensibly related quantum speed limit, and it seems to be widely believed that the Margolus-Levitin quantum speed limit can be similarly generalized to closed systems. However, a recent geometrical examination of this limit reveals that it differs significantly from most known quantum speed limits. In this paper, we show that, contrary to the common belief, the Margolus-Levitin quantum speed limit does not extend to closed systems in an obvious way. More precisely, we show that for every hypothetical bound of Margolus-Levitin type, there are closed systems that evolve with a conserved normalized expected energy between states with any given fidelity in a time shorter than the bound. We also show that for isolated systems, the Mandelstam-Tamm quantum speed limit and a slightly weakened version of this limit that we call the Bhatia-Davies quantum speed limit always saturate simultaneously. Both of these evolution time estimates extend straightforwardly to closed systems. We demonstrate that there are closed systems that saturate the Mandelstam-Tamm but not the Bhatia-Davies quantum speed limit.
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