Related papers: MIP*=RE
We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of $1$ in the game can only be achieved in the limit of strategies using arbitrarily…
The behavior of games repeated in parallel, when played with quantumly entangled players, has received much attention in recent years. Quantum analogues of Raz's classical parallel repetition theorem have been proved for many special…
The Connes Embedding Problem (CEP) is a problem in the theory of tracial von Neumann algebras and asks whether or not every tracial von Neumann algebra embeds into an ultrapower of the hyperfinite II$_1$ factor. The CEP has had interactions…
The class of languages having polynomial-time classical or quantum interactive proof systems ($\mathsf{IP}$ or $\mathsf{QIP}$, respectively) is identical to $\mathsf{PSPACE}$. We show that $\mathsf{PSPACE}$ (and so $\mathsf{QIP}$) is subset…
The landmark quantum complexity result MIP$^*$=RE was used to prove the existence of a non Connes embeddable tracial von Neumann algebra. Recently, similar ideas were used to give a negative solution to the Aldous-Lyons conjecture: there is…
Nonlocal games are a foundational tool for understanding entanglement and constructing quantum protocols in settings with multiple spatially separated quantum devices. In this work, we continue the study initiated by Kalai et al. (STOC '23)…
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 $t$-player XOR games for which the entangled bias is $1$ but for which…
The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra $\cal O_2$. Motivated by the recent refutation of the Connes Embedding Problem using the quantum complexity result MIP*=RE, we…
We investigate the connection between the complexity of nonlocal games and the arithmetical hierarchy, a classification of languages according to the complexity of arithmetical formulas defining them. It was recently shown by Ji, Natarajan,…
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…
We consider one-round games between a classical verifier and two provers. One of the main questions in this area is the \emph{parallel repetition question}: If the game is played $\ell$ times in parallel, does the maximum winning…
This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that…
We present two parallel repetition theorems for the entangled value of multi-player, one-round free games (games where the inputs come from a product distribution). Our first theorem shows that for a $k$-player free game $G$ with entangled…
We present a strong parallel repetition theorem for the entangled value of multi-player, one-round free games (games where the inputs come from a product distribution). Our result is the first parallel repetition theorem for entangled games…
In their recent breakthrough result, Slofstra and the second author show that there is a two-player one-round perfect zero-knowledge MIP* protocol for RE (STOC'24). We build on their result to show that there exists a succinct two-player…
Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…
Complexity class containments involving interactive proof classes are famously nonrelativizing: although $\mathsf{IP} = \mathsf{PSPACE}$, Fortnow and Sipser showed that that there exists an oracle relative to which $\mathsf{coNP}…
This paper considers the decidability of fully quantum nonlocal games with noisy maximally entangled states. Fully quantum nonlocal games are a generalization of nonlocal games, where both questions and answers are quantum and the referee…
XOR games are the simplest model in which the nonlocal properties of entanglement manifest themselves. When there are two players, it is well known that the bias --- the maximum advantage over random play --- of entangled players can be at…
The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared between provers affects the verification power of the proof system. We study for the first time positive aspects of prior…