Citation: Shi, Bowen. "Seeing topological entanglement through the information convex." Physical Review Research 1.3 (2019): 033048.
Web: https://arxiv.org/abs/1810.01986
Tags: Information-theory, MTC-reconstruction
This paper gives a treatment of the basics of the algebraic theory of topological quantum information in terms of, well, quantum information!
A gapped Hamiltonian is chosen from the outset, and the author puts a huge number of restrictions on it. These restrictions paint a picture - they give a direct link between the algebraic theory and the entanglement of local ground states. After setting up all of these restrictions, the author then shows that the conditions are powerful enough to start proving theorems. In particular, he shows that certain von Neumann entanglement quantities are related to quantum dimension, he demonstrates the probabilistic interpretation of quantum dimension/fusion coefficients, and he proves circuit-depth lower bounds on non-abelian anyon creation operators. The circuit-depth lower bound is similar to the one in
> Bravyi, Sergey, Matthew B. Hastings, and Frank Verstraete. "Lieb-Robinson bounds and the generation of correlations and topological quantum order." Physical review letters 97.5 (2006): 050401.
The main tool of this paper is the information convex. The restrictions are modeled off of the results from
> Shi, Bowen, and Yuan-Ming Lu. "Characterizing topological order by the information convex." Physical Review B 99.3 (2019): 035112.
which can be roughly summarized as the fact the Kitaev quantum double model satisfies all of the restrictions imposed in this paper.