Weaving and neural complexity in symmetric quantum states

TL;DR

This paper investigates two measures of quantum correlation complexity, weaving and neural complexity, in symmetric quantum states, providing formulas for GHZ states mixed with noise to understand their behavior.

Contribution

It extends neural complexity to quantum states and derives explicit formulas for these measures in noisy GHZ states, advancing understanding of quantum correlation patterns.

Findings

Derived closed-form formulas for weaving and neural complexity in GHZ states with noise.

Extended neural complexity concept from classical to quantum systems.

Analyzed the behavior of correlation measures in symmetric quantum states.

Abstract

We study the behaviour of two different measures of the complexity of multipartite correlation patterns, weaving and neural complexity, for symmetric quantum states. Weaving is the weighted sum of genuine multipartite correlations of any order, where the weights are proportional to the correlation order. The neural complexity, originally introduced to characterize correlation patterns in classical neural networks, is here extended to the quantum scenario. We derive closed formulas of the two quantities for GHZ states mixed with white noise.