论文标题
最终速度限制了操作员复杂性的增长
Ultimate Speed Limits to the Growth of Operator Complexity
论文作者
论文摘要
在一个孤立的系统中，在海森堡图片中可观察到的给定的时间演变可以在克里洛夫空间中有效地表示。在此表示形式中，随着时间的流逝，初始操作员变得越来越复杂，可以通过Krylov复杂性来量化的功能。我们通过制定Robertson的不确定性关系，涉及Krylov复杂性操作员和Liouvillian作为时间演化的发生者，从而对Krylov复杂性的增长引入了基本和普遍的限制。我们进一步显示了该条件的限制，并在量子混乱的范式模型中说明了其有效性。
In an isolated system, the time evolution of a given observable in the Heisenberg picture can be efficiently represented in Krylov space. In this representation, an initial operator becomes increasingly complex as time goes by, a feature that can be quantified by the Krylov complexity. We introduce a fundamental and universal limit to the growth of the Krylov complexity by formulating a Robertson uncertainty relation, involving the Krylov complexity operator and the Liouvillian, as generator of time evolution. We further show the conditions for this bound to be saturated and illustrate its validity in paradigmatic models of quantum chaos.
