相关论文: Anchored parallel repetition for nonlocal games

In this work we construct tests that allow a classical user to certify high dimensional entanglement in uncharacterized and possibly noisy quantum devices. We present a family of non-local games $\{G_n\}$ that for all $n$ certify states…

We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to…

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…

In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint…

Quantum game theory is a new interdisciplinary field between game theory and physical research. In this paper, we extend the classical inspection game into a quantum game version by quantizing the strategy space and importing entanglement…

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…

We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from…

A binary constraint system game is a two-player one-round non-local game defined by a system of Boolean constraints. The game has a perfect quantum strategy if and only if the constraint system has a quantum satisfying assignment [R. Cleve…

Non-locality is a feature of quantum mechanics that cannot be explained by local realistic theory. It can be detected by the violation of Bell's inequality. In this work, we have considered the evaluation of Bell's inequality with the help…

It is known that repeated gambling over the outcomes of independent and identically distributed (i.i.d.) random variables gives rise to alternate operational meaning of entropies in the classical case in terms of the doubling rates. We give…

We present and study a variant of the mean payoff games introduced by A. Ehrenfeucht and J. Mycielski. In this version, the second player makes an infinite sequence of moves only after the first player's sequence of moves has been decided…

Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending…

We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…

We investigate the 3-player quantum Prisoner's Dilemma with a certain strategic space, a particular Nash equilibrium that can remove the original dilemma is found. Based on this equilibrium, we show that the game is enhanced by 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 develop a resource-theoretical approach that allows us to quantify values of two-player, one-round cooperative games with quantum inputs and outputs, as well as values of quantum probabilistic hypergraphs. We analyse the quantum game…

Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the…

We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…

We propose a scheme for a quantum game based on performing an EPR type experiment and in which each player's spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the…

In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…