Playing games with EPR-type experiments

Playing Quantum Monty Hall Game in a Quantum Computer

Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering work, Flitney and Abbott [Phys. Rev. A 65, 062318 (2002)] showed that by using a maximally entangled system for Alice and Bob's choices, and using quantum strategies, Bob and Alice can win or lose depending on the strategy chosen by either of the players. Here we develop a new quantum algorithm with quantum circuits for playing the quantum Monty Hall game by a …

Probabilistic analysis of three-player symmetric quantum games played using the Einstein-Podolsky-Rosen-Bohm setting

This paper extends our probabilistic framework for two-player quantum games to the mutliplayer case, while giving a unified perspective for both classical and quantum games. Considering joint probabilities in the standard Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting for three observers, we use this setting in order to play general three-player non-cooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities provided by the EPR-Bohm setting can change the outcome of a game, while requiring that the quantum game attains a classical interpretation for factoriza…

Quantum Matching Pennies Game

A quantum version of the Matching Pennies (MP) game is proposed that is played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct the quantum game without using the state vectors, while considering only the quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We embed the classical game within the quantum game such that the classical MP game results when the quantum mechanical joint probabilities become factorizable. We report new Nash equilibria in the quantum MP game that emerge when the quantum mechanical joint probabilities maximally violate the Clau…

Playing quantum nonlocal games with six noisy qubits on the cloud

Nonlocal games are extensions of Bell inequalities, aimed at demonstrating quantum advantage. These games are well suited for noisy quantum computers because they only require the preparation of a shallow circuit, followed by the measurement of non-commuting observable. Here, we consider the minimal implementation of the nonlocal game proposed in Science 362, 308 (2018). We test this game by preparing a 6-qubit cluster state using quantum computers on the cloud by IBM, Ionq, and Honeywell. Our approach includes several levels of optimization, such as circuit identities and error mitigation and…

Playing Games with Quantum Mechanics

We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspectiv…

Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability

Game-playing proofs constitute a powerful framework for non-quantum cryptographic security arguments, most notably applied in the context of indifferentiability. An essential ingredient in such proofs is lazy sampling of random primitives. We develop a quantum game-playing proof framework by generalizing two recently developed proof techniques. First, we describe how Zhandry's compressed quantum oracles~(Crypto'19) can be used to do quantum lazy sampling of a class of non-uniform function distributions. Second, we observe how Unruh's one-way-to-hiding lemma~(Eurocrypt'14) can also be applied t…

使用可分离量子态比任何经典关联更好地玩贝叶斯游戏

Playing Bayesian games better with separable quantum states than with any classical correlation

研究贝叶斯游戏中关联对玩家的影响，发现可分离量子态能创造优于经典关联均衡的新量子均衡，证明非经典关联是资源，让游戏中的量子优势更易实现。

Constructing multi-player quantum games from non-factorizable joint probabilities

We use the standard three-party Einstein-Podolsky-Rosen (EPR) setting in order to play general three-player non-cooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities that may emerge in the EPR setting can change outcome of the game. Our setup requires that the quantum game attains classical interpretation for factorizable joint probabilities. We analyze the generalized three-player game of Prisoner's Dilemma (PD) and show that the players can indeed escape from the classical outcome of the game because of non-factorizable joint probabilities. This result…

Test for a large amount of entanglement, using few measurements

Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement, n EPR states. The test is efficient: unlike earlier tests that play many games, in sequence or in parallel, our test requires only one or two CHSH games. One system is directed to play a CHSH game on a random specified qubit i, and the other is told to play games on qubits {i,j}, without knowing which index is i. The test is robust: a success probability within delta of optimal guarantees distance O(n^{5/2…

Constructing quantum games from non-factorizable joint probabilities

A probabilistic framework is developed that gives a unifying perspective on both the classical and the quantum games. We suggest exploiting peculiar probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct quantum games. In our framework a game attains classical interpretation when joint probabilities are factorizable and a quantum game corresponds when these probabilities cannot be factorized. We analyze how non-factorizability changes Nash equilibria in two-player games while considering the games of Prisoner's Dilemma, Stag Hunt, and Chicken. In this framework we fin…

Playing Prisoner's Dilemma with Quantum Rules

Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum games in different conditions, i.e. different number of the players, different strategic space of the players and different amount of the entanglement involved.

Playing a quantum game with a corrupted source

The quantum advantage arising in a simplified multi-player quantum game, is found to be a disadvantage when the game's qubit-source is corrupted by a noisy "demon". Above a critical value of the corruption-rate, or noise-level, the coherent quantum effects impede the players to such an extent that the optimal choice of game changes from quantum to classical.

A doubly exponential upper bound on noisy EPR states for binary games

This paper initiates the study of a class of entangled games, mono-state games, denoted by $(G,ψ)$, where $G$ is a two-player one-round game and $ψ$ is a bipartite state independent of the game $G$. In the mono-state game $(G,ψ)$, the players are only allowed to share arbitrary copies of $ψ$. This paper provides a doubly exponential upper bound on the copies of $ψ$ for the players to approximate the value of the game to an arbitrarily small constant precision for any mono-state binary game $(G,ψ)$, if $ψ$ is a noisy EPR state, which is a two-qubit state with completely mixed states as marginal…

Playing games in quantum mechanical settings: A necessary and sufficient condition

A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy, 2x2, dilemma containing classical games, and transferred them into quantum realm showing that in quantum pure strategies dilemmas in such games can be resolved if entanglement is distributed between the players armed with quantum operations. Moreover, it became clear that the players receive the highest sum of payoffs available in the game, which are otherwise…

Playing a true Parrondo's game with a three state coin on a quantum walk

Playing a Parrondo's game with a qutrit is the subject of this paper. We show that a true quantum Parrondo's game can be played with a 3 state coin(qutrit) in a 1D quantum walk in contrast to the fact that playing a true Parrondo's game with a 2 state coin(qubit) in 1D quantum walk fails in the asymptotic limits.

Quantum computer: an appliance for playing market games

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game theory. The paper contain an analysis of such markets that shows that there would be advantage in using quantum computers and quantum strategies.

Playing a quantum game on polarization vortices

The quantum mechanical approach to the well known prisoners dilemma, one of the basic examples to illustrate the concepts of Game Theory, is implemented with a classical optical resource, nonquantum entanglement between spin and orbital degrees of freedom of laser modes. The concept of entanglement is crucial in the quantum version of the game, which brings novel features with a richer universe of strategies. As we show, this richness can be achieved in a quite unexpected context, namely that of paraxial spin-orbit modes in classical optics.

与宇宙掷骰子：用量子计算机玩传统游戏

Playing Dice with the Universe: Programming Quantum Computers to Play Traditional Games

利用量子计算机编程玩传统游戏，通过隐式表示所有可能路径来识别最优策略，无需硬编码或机器学习策略。

Quantum repeated games revisited

We present a scheme for playing quantum repeated 2x2 games based on the Marinatto and Weber's approach to quantum games. As a potential application, we study twice repeated Prisoner's Dilemma game. We show that results not available in classical game can be obtained when the game is played in the quantum way. Before we present our idea, we comment on the previous scheme of playing quantum repeated games.

Playing nonlocal games with phases of quantum matter

The parity game is an example of a nonlocal game: by sharing a Greenberger-Horne-Zeilinger (GHZ) state before playing this game, the players can win with a higher probability than is allowed by classical physics. The GHZ state of $N$ qubits is also the ground state of the ferromagnetic quantum Ising model on $N$ qubits in the limit of vanishingly weak quantum fluctuations. Motivated by this observation, we examine the probability that $N$ players who share the ground state of a generic quantum Ising model, which exhibits non-vanishing quantum fluctuations, still win the parity game using the p…

在量子计算机上跨越拓扑相变玩非定域博弈

Playing nonlocal games across a topological phase transition on a quantum computer

本文引入一族多人量子博弈，将拓扑有序相作为产生量子优势的资源，并在Quantinuum H1-1量子计算机上利用变形toric code状态实验验证了其跨越拓扑相变时对局部扰动的鲁棒性。