论文标题
针对克里洛夫州和运营商复杂性的普遍方法
A universal approach to Krylov State and Operator complexities
论文作者
论文摘要
我们提出了一个一般框架，其中Krylov州和操作员的复杂性都可以放置在同一基础上。在我们的形式主义中，Krylov的复杂性是根据相关状态的密度矩阵来定义的，该状态的密度矩阵对于操作员的复杂性而言，其生活在通过通道状态图获得的双倍的希尔伯特空间上。从密度矩阵的角度来看，这种复杂性的统一定义使我们能够将Krylov复杂性的概念扩展到子区域或状态复杂性，并且自然而然地对Krylov相互复杂性。我们表明，该框架还很好地包含了复杂性的全息概念。
We present a general framework in which both Krylov state and operator complexities can be put on the same footing. In our formalism, the Krylov complexity is defined in terms of the density matrix of the associated state which, for the operator complexity, lives on a doubled Hilbert space obtained through the channel-state map. This unified definition of complexity in terms of the density matrices enables us to extend the notion of Krylov complexity, to subregion or mixed state complexities and also naturally to the Krylov mutual complexity. We show that this framework also encompasses nicely the holographic notions of complexity.
