7 problems

CoRE-hardness conjecture. Deciding which of these two cases holds is $\mathrm{coRE}$-hard; equivalently, $\mathrm{MIP}^{\mathrm{co}}=\mathrm{coRE}$.

Let $\mcG_1$ and $\mcG_2$ be two synchronous games. Robust product self-testing conjecture. The product game $\mcG_1\times\mcG_2$ is a robust self-test for its perfect strategies i…

Consider the noncommutative polynomial problem defining the unitary capacity in Sections 4 and 5, with its tensor-product and commuting operator values. Equality conjecture. The te…

The Torpedo Game is a prepare-and-measure game in dimension $d$, where classical strategies assign answers subject to the game's consistency conditions, and a strategy is perfect w…

Physical transformation conjecture. There is an analogous physical transformation using an infinite-dimensional entangled state in the commuting operator framework.

Let $\mathscr{G}=(G_n)_{n\in\mathbb{N}}$ be a sequence of nonlocal games, and let the complexity of a sequence refer to the complexity of its $n$th game. Gap-preserving compression…

Let $\mathcal{M}$ be a Turing machine that does not halt on an empty input tape, and let $\mathfrak{G}_{\mathcal{M}}$ be the corresponding nonlocal game. Write…