Title: Everything Everywhere All at Once: Holographic Entropy Inequalities, the Topology of Error Correction, Black Holes, Cubohemioctahedron, and (maybe) the Toric Code

Speaker: Bartek Czechn (Tsinghua University)

Time: 2:00 pm, Oct 26 (Thursday) 2023

Location: 理科楼C302

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.

Bio: Bartek Czech joined the Institute for Advanced Study at Tsinghua University in 2018. Before that, he had been a postdoc at IAS-Princeton, Stanford, and other places. He studies applications of quantum information theory to the AdS/CFT correspondence.