# OTOC, complexity and entropy in bi-partite systems

## TL;DR

This paper investigates the relationship between out-of-time ordered correlators (OTOCs), Wigner separability entropy (WSE), and classical entropy in bipartite quantum systems, revealing their similar behavior and establishing a theoretical link between them.

## Contribution

It demonstrates that OTOCs and WSE exhibit similar dynamics in bipartite systems and connects these measures through a theorem relating Renyi entropy and OTOCs, advancing understanding of quantum complexity.

## Key findings

- OTOCs and WSE show similar behavior in bipartite systems.
- Both measures effectively characterize quantum complexity.
- A theoretical link between OTOCs and Renyi entropy is established.

## Abstract

There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics, for example. The exponential growth has been verified for many paradigmatic maps and systems. But less is known for multi-partite cases. On the other hand the recently introduced Wigner separability entropy (WSE) and its classical counterpart (CSE) provide with a complexity measure that treats equally quantum and classical distributions in phase space. We have compared the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic (HH), double elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and the WSE have essentially the same behavior, providing with a complete characterization in generic bi-partite systems and at the same time revealing them as very good measures of quantum complexity for phase space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Renyi entropy and OTOCs.