Stabilizer States and the Holographic Entropy Cone

Abstract

The quantum entropy cone encapsulates all possible entropic structures for quantum states. The linear entropy inequalities that define it are a subset of those that define the analogous structure for holographic states: the holographic entropy cone. We define and review all of these concepts. Given the connection between AdS/CFT holography and quantum error correction, we seek to characterize the holographic entropy cone through a class of quantum states primarily used in quantum error correcting codes: qudit stabilizer states. We develop prerequisite formalism for the analysis of stabilizer states and especially their entanglement entropies. Then, we focus on a subset of stabilizer states called XZ-separable stabilizer states in order to simplify the expression for entanglement entropy. Finally, we look at ways of constructing XZ-separable states from entropy vectors, and apply this to many of the extreme rays of the 5-region holographic entropy cone.