Abstract

An important class of quantum states are those whose entanglement entropies can be computed by minimal cuts through some bulk structure—-a holographic spacetime or a random tensor network. Such states obey linear constraints on their entanglement entropies, which are known as holographic entropy inequalities. I present two new infinite families of holographic entropy inequalities. The entropies featured in these inequalities are best visualized on graphs whose incidence relations reflect subsystem inclusion. These graphs turn out to be tessellations of the torus and the real projective plane. The non-contractible cycles on these manifolds play an indispensable role in proving the inequalities, which shows that they hold for essentially topological reasons. Physically, the inequalities represent constraints on holographic error correcting codes and, in some cases, the entropy of two-sided black holes. If time allows it, I will sketch bonus applications, which involve a non-planar polytope called “cubohemioctahedron” and (more speculatively) the toric code.Co-authors: Sirui Shuai, Yixu Wang, Daiming Zhang