Recently, Bravyi, Gosset, and Konig (Science, 2018) exhibited a search problem called the
2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant …

Understanding and approximating extremal energy states of local Hamiltonians is a central
problem in quantum physics and complexity theory. Recent work has focused on developing …

In this paper, we prove a quantum union bound that is relevant when performing a sequence
of binary-outcome quantum measurements on a quantum state. The quantum union bound …

This paper considers a special class of nonlocal games (G,ψ), where G is a two-player one-
round game, and ψ is a bipartite state independent of G. In the game (G,ψ), the players are …

We consider 3XOR games with perfect commuting operator strategies. Given any 3XOR
game, we show existence of a perfect commuting operator strategy for the game can be …

Optimization is a fundamental area in mathematics and computer science, with many real-
world applications. In this thesis we study the efficiency with which we can solve certain …

We bound separations between the entangled and classical values for several classes of
nonlocal $ t $-player games. Our motivating question is whether there is a family of $ t …

We give an $\dfrac {1}{54} $ separation between 5-party pseudo-telepathy games and two-
local theories. We define the notion of strategy in a k-local theory for a game, and extend the …

In this dissertation, we study quasirandomness in several contexts, mostly in quantum
information theory. An object is quasirandom if it shares properties with a random object …

This honors thesis arose from an undertaking to determine the critical threshold of 3XOR
game (if it exists). A game amounts to a special system of m equations with 3n unknowns …