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

Speaker: Bartek Czech

Affiliation: IAS, Tsinghua University (清华大学高等研究院）

Time: 14:00-15:00, Thursday, 21st March, 2024 (UTC+8, Beijing Time)

Venue: Room 1502, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing

           （东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）

             Zoom Meeting (ID: 385 442 0225; Passcode: yauc)    (Offline and online)

Inviter: Qiang Wen （文强）

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.

Speaker

Professor Bartek Czech is currently a faculty member at the Institute for Advanced Study, Tsinghua University.

His personal webpage: https://www.ias.tsinghua.edu.cn/en/info/1059/1176.htm

The seminar will be broadcasted online by Zoom.

Interested people are free to join, without registration in advance.

The Zoom info is

URL: https://us02web.zoom.us/j/3854420225?pwd=SXY4eWJKOTBFZWJDaE16aXpTamY1QT09

Meeting ID: 385 442 0225

Passcode: yauc