A group with at least subexponential hyperlinear profile

Abstract

The hyperlinear profile of a group measures the growth rate of the dimension of unitary approximations to the group. We construct a finitely-presented group whose hyperlinear profile is at least subexponential, i.e. at least $\exp (1/{\epsilon }^k)$ for some $0<k<1$. We use this group to give an example of a two-player non-local game requiring subexponential Hilbert space dimension to play near-perfectly.

13 pages

References in corpus (3)

• Perfect Commuting-Operator Strategies for Linear System Games
• Operator algebraic approach to inverse and stability theorems for amenable groups
• Entanglement in non-local games and the hyperlinear profile of groups

Cited by in corpus (1)

• Quantum dimension test using the uncertainty principle