运算符复杂性增长的极限速度
Ultimate Speed Limits to the Growth of Operator Complexity
摘要：
在一个孤立系中，海森堡图像中给定观测量的时间演化可以有效地在Krylov空间中表示。在这种表示中，初始算子随着时间的推移变得越来越复杂，这一特征可以通过Krylov复杂度来量化。我们引入了一个基本的和普遍的限制的增长的Krylov复杂性制定罗伯逊不确定性关系，涉及Krylov复杂性运营商和Liouvillian，作为发电机的时间演化。我们进一步显示的条件，这个限制是饱和的，并说明其有效性的量子混沌的范例模型。
英文摘要：
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.
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