# Area law, topological quantum field theory, and the quantum marginal problem

### APA

Kim, I. (2021). Area law, topological quantum field theory, and the quantum marginal problem. Perimeter Institute. https://pirsa.org/21020024

### MLA

Kim, Isaac. Area law, topological quantum field theory, and the quantum marginal problem. Perimeter Institute, Feb. 16, 2021, https://pirsa.org/21020024

### BibTex

@misc{ pirsa_PIRSA:21020024, doi = {10.48660/21020024}, url = {https://pirsa.org/21020024}, author = {Kim, Isaac}, keywords = {Quantum Information}, language = {en}, title = {Area law, topological quantum field theory, and the quantum marginal problem}, publisher = {Perimeter Institute}, year = {2021}, month = {feb}, note = {PIRSA:21020024 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

Many physical states of interest, such as ground states of gapped quantum many-body systems, are expected to obey an area law of entanglement entropy. I will report on a series of recent results that suggest a deep connection between area law and two seemingly unrelated subjects: topological quantum field theory and quantum marginal problem. Recently, we deduced --- only using area law and quantum information-theoretic tools --- the existence of new topological charges and invariants associated with the domain walls between topologically ordered systems in two spatial dimensions. Moreover, the same set of tools were also used in finding a solution to the quantum marginal problem. This is the problem in which one asks whether a set of reduced density matrices on bounded subsystems are compatible with some globally well-defined many-body quantum state. Since this problem was first posed in 1959, a solution that goes beyond the mean-field ansatz has remained elusive until now. These results suggest that area law is not just a qualitative statement about entanglement; it is an important equation that lets us "solve" quantum many-body systems that appear in nature.

Based on arXiv:2008.11793 and arXiv:2010.07424