Navigating the Quantum Resource Landscape of Entropy Vector Space Using Machine Learning and Optimization

TL;DR

This paper introduces a machine learning and optimization framework to explore quantum entropy vectors, identify violations of entropy inequalities like Ingleton's, and analyze the structure of quantum resource states.

Contribution

It develops a novel reinforcement learning approach combined with classical optimization to find and characterize quantum states violating entropy inequalities.

Findings

Identified quantum circuits that maximize Ingleton inequality violations.

Discovered Ingleton-violating states are rare and occupy isolated regions in Hilbert space.

Provided a computational toolkit for studying entropy vector dynamics and quantum resource engineering.

Abstract

We present a machine learning framework to study the dynamics of entropy vectors and quantum resources, including entanglement and magic, focusing on violations of entropy inequalities. Using a reinforcement learning agent formulated as a Markov decision process, we identify quantum circuits that optimally navigate the entropy vector space to generate violations of Ingleton's inequality. We complement this approach with a classical optimization algorithm to produce arbitrary numbers of Ingleton-violating states, with tunable degrees of violation, and empirically determine the maximal attainable violation for Ingleton's inequality. Our analysis reveals characteristic patterns of quantum resources that accompany Ingleton violation. A comprehensive statistical analysis shows that Ingleton-violating states occupy sharply-defined, isolated regions of the Hilbert space, and are extremely rare. Together, these results establish a unified computational toolkit for studying entropy vector dynamics, tracking quantum resource evolution, and engineering circuits with controlled information-theoretic features.