# Universal lower bound on topological entanglement entropy

### APA

Kim, I. (2023). Universal lower bound on topological entanglement entropy. Perimeter Institute. https://pirsa.org/23030109

### MLA

Kim, Isaac. Universal lower bound on topological entanglement entropy. Perimeter Institute, Mar. 29, 2023, https://pirsa.org/23030109

### BibTex

@misc{ pirsa_PIRSA:23030109, doi = {10.48660/23030109}, url = {https://pirsa.org/23030109}, author = {Kim, Isaac}, keywords = {Quantum Information}, language = {en}, title = {Universal lower bound on topological entanglement entropy}, publisher = {Perimeter Institute}, year = {2023}, month = {mar}, note = {PIRSA:23030109 see, \url{https://pirsa.org}} }

Isaac Kim University of California, Davis

## Abstract

Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that characterizes the underlying topological phase. However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase. The difference between the TEE and the value predicted by the anyon theory is often called the spurious topological entanglement entropy. We show this spurious contribution is always nonnegative, thus the value predicted by the anyon theory provides a universal lower bound. This observation also leads to a definition of TEE which is invariant under constant-depth quantum circuits.

Based on a joint work with Daniel Ranard (MIT), Michael Levin (U Chicago), Ting-Chun Lin (UCSD), and Bowen Shi (UCSD)

Zoom link: https://pitp.zoom.us/j/93809342984?pwd=QXJkK0ZYR3QzdjlUUWlkMEFXMWRnQT09