Related papers: Connes implies Tsirelson: a simple proof
In the context of multiplayer games, the parallel repetition problem can be phrased as follows: given a game $G$ with optimal winning probability $1-\alpha$ and its repeated version $G^n$ (in which $n$ games are played together, in…
A central question in quantum information theory and computational complexity is how powerful nonlocal strategies are in cooperative games with imperfect information, such as multi-prover interactive proof systems. This paper develops a new…
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…
Robust self-testing in non-local games allows a classical referee to certify that two untrustworthy players are able to perform a specific quantum strategy up to high precision. Proving robust self-testing results becomes significantly…
We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the…
Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…
This paper, and its companion [BCLV24], are devoted to a negative resolution of the Aldous--Lyons Conjecture [AL07, Ald07]. In this part we study tailored non-local games. This is a subclass of non-local games -- combinatorial objects which…
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)…
The study of quantum correlation sets initiated by Tsirelson in the 1980s and originally motivated by questions in the foundations of quantum mechanics has more recently been tied to questions in quantum cryptography, complexity theory,…
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…
We review the correspondence between synchronous games and their associated $*$-algebra. Building upon the work of (Helton et al., New York J. Math. 2017), we propose results on algebraic and locally commuting graph identities. Based on the…
We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical…
We unify and consolidate various results about non-signall-ing games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general theorems about them, which extend a…
In this note, we consider quantum correlations of bipartite systems having a slight interaction, and reinterpret Tsirelson's problem (and hence Kirchberg's and Connes's conjectures) in terms of finite-dimensional asymptotically commuting…
We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that…
We study three problems related to the computational complexity of the popular game Minesweeper. The first is consistency: given a set of clues, is there any arrangement of mines that satisfies it? This problem has been known to be…
We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant…
We construct a linear system non-local game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert space, or even with any tensor-product…
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…
We show that the *-algebra of the product of two synchronous games is the tensor product of the corresponding *-algebras. We prove that the product game has a perfect C*-strategy if and only if each of the individual games does, and that in…