Related papers: Bisynchronous Games and Factorizable Maps
We establish several strong equivalences of synchronous non-local games, in the sense that the corresponding game algebras are $*$-isomorphic. We first show that the game algebra of any synchronous game on $n$ inputs and $k$ outputs is…
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…
We show that the C*-algebras associated with synchronous games give rise to certain quantum families of maps between the input and output sets of the game. In particular situations (e.g. for graph endomorphism games) these quantum families…
We introduce concurrent quantum non-local games, quantum output mirror games and concurrent classical-to-quantum non-local games, as quantum versions of synchronous non-local games, and provide tracial characterisations of their perfect…
In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon…
We study a class of nonlocal games, called transitive games, for which the set of perfect strategies forms a semigroup. We establish several interesting correspondences of bisynchronous transitive games with the theory of compact quantum…
We generalize Banica's construction of the quantum isometry group of a metric space to the class of quantum metric spaces in the sense of Kuperberg and Weaver. We also introduce quantum isometries between two quantum metric spaces, and we…
Using the simulation paradigm in information theory, we define notions of quantum hypergraph homomorphisms and quantum hypergraph isomorphisms, and show that they constitute partial orders and equivalence relations, respectively.…
Synchronous correlations provide a class of nonlocal games that behave like functions between finite sets. In this work we examine categories whose morphisms are games with synchronous classical, quantum, or general nonsignaling…
We introduce a two-player nonlocal game, called the $(G,H)$-isomorphism game, where classical players can win with certainty if and only if the graphs $G$ and $H$ are isomorphic. We then define the notions of quantum and non-signalling…
Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a "quantum-classical game"--that is, a non-local game of two…
We present a strong connection between quantum information and quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups, and then show…
We study the graph isomorphism game that arises in quantum information theory from the perspective of bigalois extensions of compact quantum groups. We show that every algebraic quantum isomorphism between a pair of (quantum) graphs $X$ and…
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…
A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding…
We define a general framework of partition games for formulating two-player pebble games over finite structures. We show that one particular such game, which we call the invertible-map game, yields a family of polynomial-time approximations…
We define and study a collection of matroid isomorphism games corresponding to various axiomatic characterizations of matroids. These are nonlocal games played between two cooperative players. Each game is played on two matroids, and the…
We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…
We introduce classical and quantum no-signalling bicorrelations and characterise the different types thereof in terms of states on operator system tensor products, exhibiting connections with bistochastic operator matrices and with…
Inspired by asynchronous cooperative Parrondo's games we introduce two new types of games in which all players simultaneously play game A or game B or a combination of these two games. These two types of games differ in the way a…