A quantum complexity approach to the Kirchberg Embedding Problem
Operator Algebras
2023-03-03 v2 Computational Complexity
Logic
Abstract
The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra . Motivated by the recent refutation of the Connes Embedding Problem using the quantum complexity result MIP*=RE, we establish two quantum complexity consequences of a positive solution to KEP. Both results involve almost-commuting strategies to nonlocal games.
Cite
@article{arxiv.2107.14010,
title = {A quantum complexity approach to the Kirchberg Embedding Problem},
author = {Isaac Goldbring and Bradd Hart},
journal= {arXiv preprint arXiv:2107.14010},
year = {2023}
}
Comments
A referee pointed out that the first theorem can be obtained using elementary means in a manner not connected to the KEP. The second result will be incorporated into a new paper that will appear on the arxiv shortly