Related papers: The quantum-to-classical graph homomorphism game
In this work we propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values. The developed quantum scheme is then used to study the expected…
We analyze a continuous-time quantum walk on a chimera graph, which is a graph of choice for designing quantum annealers, and we discover beautiful quantum-walk features such as localization that starkly distinguishes classical from quantum…
In some scenarios ("anti-coordination games"), individuals are better off choosing different actions than their neighbors while in other scenarios ("coordination games"), it is beneficial for individuals to choose the same strategy as their…
Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information…
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…
Counting homomorphisms from a graph $H$ into another graph $G$ is a fundamental problem of (parameterized) counting complexity theory. In this work, we study the case where \emph{both} graphs $H$ and $G$ stem from given classes of graphs:…
For graphs $G$ and $H$, an {\em $H$-colouring} of $G$ (or {\em homomorphism} from $G$ to $H$) is a function from the vertices of $G$ to the vertices of $H$ that preserves adjacency. $H$-colourings generalize such graph theory notions as…
Quantum pseudotelepathy is a strong form of nonlocality. Different from the conventional non-local games where quantum strategies win statistically, e.g., the Clauser-Horne-Shimony-Holt game, quantum pseudotelepathy in principle allows…
The semi-random graph process is a single-player game that begins with an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then adaptively selects a vertex…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
This paper studies correlations among independently administered hypothetical tests of a simple interactive type, and demonstrates that correlations arising in quantum information theoretic variants of these tests can exhibit a striking…
This paper investigates the role of interaction and coins in public-coin quantum interactive proof systems (also called quantum Arthur-Merlin games). While prior works focused on classical public coins even in the quantum setting, the…
We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such…
We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
We study the relation between the quantum games, communication complexity problems and Bell inequalities. In particular we are interested in answering the question whether for every element of one of these groups there is a corresponding…
Quantum game theory lays a foundation for understanding the interaction of people using quantum computers with conflicting interests. Recently Zhang proposed a simple yet rich model to study quantum strategic games, and addressed some…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…