Algorithmic Methods for Analyzing the Entropies of Stabilizer States.

The entropy cone for a class of quantum states is a convex, polyhedral cone representing the set of all entropy vectors that satisfy inequalities necessarily obeyed by that class. While previous studies have shed light into the structure of entropy cones, the relative volumes of cones corresponding to different classes of states remains largely unknown. Thus, in this work, we present foundational algorithmic methods for analyzing the entropy structures of stabilizer states, with the goal of uncovering how the holographic entropy cone is nested within the stabilizer cone. These insights would offer a quantitative understanding of certain correlations underlying the AdS/CFT correspondence, and can enable the discovery of new geometrically-verifiable holographic entropy inequalities. Our algorithms generate stabilizer state entropy vectors, identifying non-holographic states by checking for MMI compliance in each entropy vector. We implement an optimized approach, using the tableau formalism, to study entropy vector evolution and efficiently navigate the space of stabilizer entropy vectors for n>6 qubits.