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On the complexity of zero gap MIP
TLDR
This paper proves that $\mathsf{MIP}^*_0$ extends beyond the first level of the arithmetical hierarchy, and in fact is equal to $\Pi_2^0$, the class of languages that can be decided by quantified formulas of the form $\forall y \, \exists z \, R(x,y,z)$.
A generalization of CHSH and the algebraic structure of optimal strategies
TLDR
This work introduces an algebraic generalization of CHSH by viewing it as a linear constraint system (LCS) game, exhibiting self-testing properties that are qualitatively different, and gives the first example of a game that is not a self-test.
Nonlocal Games, Compression Theorems, and the Arithmetical Hierarchy
TLDR
The compression theorem yields as a byproduct an alternative proof of Slofstra's result that the set of quantum correlations is not closed, and explains how results about the complexity of nonlocal games all follow in a unified manner from a technique known as compression.
Quantum Communication Complexity
TLDR
A randomized protocol π depends both on previous messages and coin flips and must evaluate f(x, y) with probability ≥ 2/3, which is the maximum communication cost over all possible inputs evaluated on f : X × Y − → {0, 1} using the Protocol π.
Synchronous Values of Games
We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy. However, we give