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

We present a machine learning framework to study the dynamics of entropy vectors and quantum resources, including entanglement and magic, with a focus on violations of entropy inequalities. In particular, we investigate Ingleton’s inequality, which is satisfied by all stabilizer and holographic quantum states. We first prove that violation is impossible for pure states of five qubits or fewer, establishing six qubits as the minimal system size required to cross the Ingleton boundary. Using a reinforcement learning agent formulated as a Markov decision process, we identify quantum circuits that navigate entropy vector space to generate Ingleton-violating states. Complementing this approach with classical optimization, we construct large families of violating states with tunable degrees of violation and empirically determine the maximal attainable violation. Our analysis reveals a sharp resource transition: violation requires substantial total quantum magic but only modest non-local magic, and occurs in statistically rare, sharply-defined regions of Hilbert space. Together, these results establish a unified computational toolkit for probing entropy cone boundaries, tracking quantum resource evolution, and engineering circuits with controlled information-theoretic features.