The out-of-time-order correlator (OTOC) has recently become relevant in different areas where it has been linked to scrambling of quantum information and entanglement. It has also been proposed as a good indicator of quantum complexity. In this sense, the OTOC-RE theorem relates the OTOCs summed over a complete basis of operators to the second Renyi entropy. Here we have studied the OTOC-RE correspondence on physically meaningful bases like the ones constructed with the Pauli, reflection, and translation operators. The evolution is given by a paradigmatic bi-partite system consisting of two perturbed and coupled Arnold cat maps with different dynamics. We show that the sum over a small set of relevant operators is enough in order to obtain a very good approximation for the entropy and, hence, to reveal the character of the dynamics. In turn, this provides us with an alternative natural indicator of complexity, i.e., the scaling of the number of relevant operators with time. When represented in phase space, each one of these sets reveals the classical dynamical footprints with different depth according to the chosen basis.

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相关的无序相关器运算符：经典动力学的足迹

失序相关器（OTOC）最近在与量子信息加扰和纠缠联系在一起的不同领域变得越来越重要。还已经提出将其作为量子复杂性的良好指标。从这个意义上讲，OTOC-RE定理将完全基于算子求和的OTOC与第二Renyi熵相关联。在这里，我们研究了在物理上有意义的基础上的OTOC-RE对应关系，例如使用Pauli，反射和翻译运算符构造的基础。演化是由一个范例性的两部分系统完成的，该系统由两个具有不同动力学的扰动和耦合的阿诺德猫图组成。我们表明，在一小套相关算子上的总和足以获得熵的很好的近似值，从而揭示动力学的特征。反过来，这为我们提供了另一种复杂性的自然指标，即相关操作员数量随时间缩放。当在相空间中表示时，这些集合中的每一个都根据选择的基础显示具有不同深度的经典动态足迹。