Related papers: The quantum-to-classical graph homomorphism game

We propose a novel method using a quantum annealer -- an analog quantum computer based on the principles of quantum adiabatic evolution -- to solve the Graph Isomorphism problem, in which one has to determine whether two graphs are…

We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…

We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However in its quantum form…

Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in…

This paper introduces a noncommutative version of the Nullstellensatz, motivated by the study of quantum nonlocal games. It has been proved that a two-answer nonlocal game with a perfect quantum strategy also admits a perfect classical…

Go has long been considered as a testbed for artificial intelligence. By introducing certain quantum features, such as superposition and collapse of wavefunction, we experimentally demonstrate a quantum version of Go by using correlated…

Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…

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 initiate a study of random instances of nonlocal games. We show that quantum strategies are better than classical for almost any 2-player XOR game. More precisely, for large n, the entangled value of a random 2-player XOR game with n…

The graph coloring game is a two-player game in which, given a graph G and a set of k colors, the two players, Alice and Bob, take turns coloring properly an uncolored vertex of G, Alice having the first move. Alice wins the game if and…

We deal with a graph colouring problem that arises in quantum information theory. Alice and Bob are each given a $\pm1$-vector of length $k$, and are to respond with $k$ bits. Their responses must be equal if they are given equal inputs,…

Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we…

Decision-making in automated driving must consider interactions with surrounding agents to be effective. However, traditional methods often neglect or oversimplify these interactions because they are difficult to model and solve, which can…

This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…

In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…

The so called \emph{quantum game theory} has recently been proclaimed as one of the new branches in the development of both quantum information theory and game theory. However, the notion of a quantum game itself has never been strictly…

A quantum game in the Eisert scheme is defined by the payoff matrix, plus some quantum entanglement parameters. In the symmetric nonzero-sum 2x2 games, the relevant features of the game are given by two parameters in the payoff matrix, and…

We prove that any perfect quantum strategy for the two-prover game encoding a constraint satisfaction problem (CSP) can be simulated via a perfect classical strategy with an extra classical communication channel, whose size depends only on…

We study a simple graph-based classical secret sharing scheme: every player's share consists of a random key together with the encryption of the secret with the keys of his neighbours. A characterisation of the authorised and forbidden sets…

Lov\'{a}sz proved that two graphs $G$ and $H$ are isomorphic if $\hom(K,G) = \hom(K,H)$ for all graphs $K$, where $\hom(G_1,G_2)$ denotes the number of homomorphisms from $G_1$ to $G_2$. Dvo\v{r}\'{a}k showed that it suffices to count…