Multiplayer Quantum Games Research Articles

Promoting green-building development in sustainable development strategy: A multi-player quantum game approach

Sustainable development has become the development goal of all countries worldwide. Promoting green buildings in sustainable development is important to promote environment-friendly development. Considering this, we used the multi-player quantum game method to analyze the interest relationship between the developer, general construction contractor, and building materials supplier for the development of green-building and discussed the influence of the three on the game system. Furthermore, this study proposes a novel three-person quantum game model, discusses the optimal strategy selection process of the three parties with and without considering the entanglement, and uses a practical engineering case to prove the effectiveness of the proposed method. Without considering the entanglement of states, developers have the lowest willingness to invest in green-building, that is, the minimum investment of 28 million. When entanglement of states is considered and the initial state is ψini=Ĵ000, developers have the highest intention to invest in green buildings, that is, 56 million. Compared with the initial state of ψini=Ĵ111 when entanglement of states is not considered and entanglement of states is considered, developers' intention to invest in green-building shows an upward trend. The results show that entanglement can effectively prevent betrayal in the process of green-building construction. Finally, according to the meaning of quantum entanglement and quantum strategy, an “entanglement treaty” is constructed, aiming at reducing the occurrence of treachery and providing an important guarantee for encouraging green-building participants to actively participate in green-building development. This study provides a decision reference for promoting green-building construction. The proposed method is also applicable in other fields.

Doubly tagged delayed-choice tunable quantum eraser: coherence, information and measurement

We present an idea for the doubly tagged delayed-choice tunable quantum eraser in a cavity QED setup, based on fully controlled resonant as well as dispersive atom–field interactions. Two cavity fields, bound initially in the Bell state, are coupled to a three-level atom. Such an atom is initially prepared in the coherent superposition of the lower two levels and is quite capable of exhibiting Ramsey fringes if taken independently. It is shown that the coherence lost due to tagging can not only be retrieved but that the fringe visibility/path distinguishability can also be conditionally tuned in a delayed manner through local manipulation of the entangled cavity fields. The stringent condition here is the retainment of the system’s coherence during successive manipulations of the individual cavity fields. Such a quantum eraser, therefore, prominently highlights the links among all the counterintuitive features of quantum theory including the conception of time, measurement, state vector reduction, coherence and information in an unambiguous manner. The schematics can be straightforwardly extended to a multipartite scenario and employed to explore multi-player quantum games with the payoff being strangely decided through delayed choice setups.

Quantum Games under Decoherence

Quantum systems are easily influenced by ambient environments. Decoherence is generated by system interaction with external environment. In this paper, we analyse the effects of decoherence on quantum games with Eisert-Wilkens-Lewenstein (EWL) (Eisert et al., Phys. Rev. Lett. 83(15), 3077 1999) and Marinatto-Weber (MW) (Marinatto and Weber, Phys. Lett. A 272, 291 2000) schemes. Firstly, referring to the analytical approach that was introduced by Eisert et al. (Phys. Rev. Lett. 83(15), 3077 1999), we analyse the effects of decoherence on quantum Chicken game by considering different traditional noisy channels. We investigate the Nash equilibria and changes of payoff in specific two-parameter strategy set for maximally entangled initial states. We find that the Nash equilibria are different in different noisy channels. Since Unruh effect produces a decoherence-like effect and can be perceived as a quantum noise channel (Omkar et al., arXiv:1408.1477v1), with the same two parameter strategy set, we investigate the influences of decoherence generated by the Unruh effect on three-player quantum Prisoners’ Dilemma, the non-zero sum symmetric multiplayer quantum game both for unentangled and entangled initial states. We discuss the effect of the acceleration of noninertial frames on the the game’s properties such as payoffs, symmetry, Nash equilibrium, Pareto optimal, dominant strategy, etc. Finally, we study the decoherent influences of correlated noise and Unruh effect on quantum Stackelberg duopoly for entangled and unentangled initial states with the depolarizing channel. Our investigations show that under the influence of correlated depolarizing channel and acceleration in noninertial frame, some critical points exist for an unentangled initial state at which firms get equal payoffs and the game becomes a follower advantage game. It is shown that the game is always a leader advantage game for a maximally entangled initial state and there appear some points at which the payoffs become zero.

Effect of uniform acceleration on multiplayer quantum game

We investigate the influence of the Unruh effect on three-qubit quantum games. In particular, we interpret the quantum Prisoners’ Dilemma, which is a famous, non-zero sum game both for entangled and unentangled initial states and show that the acceleration of non-inertial frames disturbs the symmetry of the game. Using the various strategies, the novel Nash equilibrium is obtained at infinite acceleration (r = π/4). As a remarkable point, it is shown that in our three-player system, in contrast to the two-player quantum game in non-inertial frames (see Khan et al 2011 J. Phys. A: Math. Theor. 44 355302), there is not a dominant strategy (even classical strategy) in the game and choosing the quantum strategy by each player can be the dominant strategy depending on the kind of strategy chosen by others. Since the entangled states of particles play an important role in the quantum game, finally we argue that the results of the players depend on the degree of entanglement in the initial state of the game.

Decoherence Effects on Multiplayer Cooperative Quantum Games

We study the behavior of cooperative multiplayer quantum games [Q. Chen, Y. Wang, J.T. Liu, and K.L. Wang, Phys. Lett. A 327 (2004) 98; A.P. Flitney and L.C.L. Hollenberg, Quantum Inf. Comput. 7 (2007) 111] in the presence of decoherence using different quantum channels such as amplitude damping, depolarizing and phase damping. It is seen that the outcomes of the games for the two damping channels with maximum values of decoherence reduce to same value. However, in comparison to phase damping channel, the payoffs of cooperators are strongly damped under the influence amplitude damping channel for the lower values of decoherence parameter. In the case of depolarizing channel, the game is a no-payoff game irrespective of the degree of entanglement in the initial state for the larger values of decoherence parameter. The decoherence gets the cooperators worse off.

Multiplayer quantum games and its application as access controller in architecture of quantum computers

One of the basics tasks in computer systems is the control of access of resources. Basically, there is a finite amount of resources that can be, for example, the CPU, memory or I/O ports, and several processes requiring those resources. If there is not enough resource in order to attend the demand, some kind of control access has to be employed. In this work, recognizing the resource sharing problem as a competition, we employ a simplified multiplayer quantum game as an access controller. The proposed quantum game can be employed in the architecture of quantum computers.

The effect of quantum noise on multiplayer quantum game

It has recently been realized that quantum strategies have a great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise, resulting in decoherence. In this paper, we investigate the effect of quantum noise on a multiplayer quantum game with a certain strategic space, with all players affected by the same quantum noise at the same time. Our results show that in a maximally entangled state, a special Nash equilibrium appears in the range of 0≤p≤0.622 (p is the quantum noise parameter), and then disappears in the range of 0.622<p≤1. Increasing the amount of quantum noise leads to the reduction of the quantum player's payoff.

Multiplayer quantum games with continuous-variable strategies

Based on the extended case of the Cournot's duopoly, we investigate a case of three firms in which the different entanglement parameters can vary arbitrarily. An analytical formula is presented and some interesting features are demonstrated from it. Furthermore, we find that the quantum entanglement can make an arbitrary number of players cooperate to the largest extent.

Entanglement enhanced multiplayer quantum games

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 entanglement of its initial state.

Cooperative three- and four-player quantum games

A cooperative multi-player quantum game played by 3 and 4 players has been studied. Quantum superposed operator is introduced in this work which solves the non-zero sum difficulty in previous treatment. The role of quantum entanglement of the initial state is discussed in details.

Multiplayer quantum games

Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess an alternative form of equilibrium strategy, one which has no analog either in traditional games or even in two-player quantum games. In these ``coherent'' equilibria, entanglement shared among multiple players enables different kinds of cooperative behavior: indeed it can act as a contract, in the sense that it prevents players from successfully betraying one another.

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.