Quantum prisoner dilemma under decoherence

Chen, L.K.; Ang, Huiling; Kiang, D.; Kwek, Leong Chuan; Lo, Chi‐Fai

doi:10.1016/s0375-9601(03)01175-7

Cited by 94 publications

(87 citation statements)

References 20 publications

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“…These payoffs become the classical payoffs for δ = γ = 0 and for δ = γ = π 2 and µ = 0 these payoffs transform to the results given in the Ref [4]. It is known that decoherence has no effect on the Nash equilibrium of the game but it causes a reduction in the payoffs [3,4]. In our case it is interesting to note that this reduction of the payoffs depends on the degree of memory µ.…”

Section: Quantization In Presence Of Correlated Noisesupporting

confidence: 50%

“…This type of protocol was first applied to quantum games to show that above a certain level of decoherence the quantum player has no advantage over a classical player [2]. Later quantum version of Prisoners' Dilemma was analyzed in presence of decoherence to prove that Nash equilibrium is not affected by decoherence [3]. Recently, Flitney and Abbott [4] showed for the quantum games based on dephasing quantum channel that the advantage that a quantum player enjoys over a classical player diminishes as decoherence increases and vanishes for the maximum decoherence.…”

Section: Introductionmentioning

confidence: 99%

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Quantum games with correlated noise

Nawaz¹,

Toor²

2006

J. Phys. A: Math. Gen.

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We analyze quantum game with correlated noise through generalized quantization scheme. Four different combinations on the basis of entanglement of initial quantum state and the measurement basis are analyzed. It is shown that the advantage that a quantum player can get by exploiting quantum strategies is only valid when both the initial quantum state and the measurement basis are in entangled form. Furthermore, it is shown that for maximum correlation the effects of decoherence diminish and it behaves as a noiseless game.

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Section: Quantization In Presence Of Correlated Noisesupporting

confidence: 50%

Section: Introductionmentioning

confidence: 99%

Quantum games with correlated noise

Nawaz¹,

Toor²

2006

J. Phys. A: Math. Gen.

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“…The advantage of most of the previous quantum games are not robust against the noise [21] and the unique properties of various quantum games different from their clas- * Electronic address: stephenli74@yahoo.com.cn sical counterpart will disappear in the limit of decoherence [22,23]. However, Chen et al have discussed decoherence in quantum prisoners' dilemma [24], and found some kinds of decoherence have no effects on the Nash equilibria in the quantized prisoners' dilemma with maximally entangled states. Here, we present the simulation schemes of the quantized symmetric or asymmetric Cournot's Duopoly, in which there is not any entanglement involved.…”

Section: Introductionmentioning

confidence: 99%

Simulation of continuous variable quantum games without entanglement

Li¹

2011

J. Phys. A: Math. Theor.

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A simulation scheme of quantum version of Cournot's Duopoly is proposed, in which there is a new Nash equilibrium that may be also Pareto optimal without any entanglement involved. The unique property of this simulation scheme is decoherence-free against the symmetric photon loss. Furthermore, we analyze the effects of the asymmetric information on this simulation scheme and investigate the case of asymmetric game caused by asymmetric photon loss. A second-order phase transition-like behavior of the average profits of the firm 1 and firm 2 in Nash equilibrium can be observed with the change of the degree of asymmetry of the information or the degree of "virtual cooperation". It is also found that asymmetric photon loss in this simulation scheme plays a similar role with the asymmetric entangled states in the quantum game.

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“…However, it is difficult for a maximally entangled quantum game to be realized in practice, for no quantum system can be completely isolated from its environment. System-environment interactions should induce decoherence of quantum systems [44][45][46]. The purpose of this paper is to look for the rule for the realization of cooperation in a general quantum game.…”

Section: Introductionmentioning

confidence: 99%

The Rule for Evolution of Cooperation in Quantum Games

Sun

2009

Acta Phys. Pol. A

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Cooperation is essential to biological organizations and human society. In this paper, the conditions of dilemmas resolving by quantum strategies in the three games, Prisoners' Dilemma, Chicken Game and Stag Hunt, are presented. The rule for the evolution of cooperation in general quantum games, b/c > coth 2 γ, is put forward. The formation of the rule is similar to those of the five rules in the classical game theory summarized by Nowak. b/c is still the benefit-to-cost ratio of the altruistic act, while γ is a measure for the game's entanglement. The rule is the prerequisite for the realization of cooperation in quantum games.

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Quantum prisoner dilemma under decoherence

Cited by 94 publications

References 20 publications

Quantum games with correlated noise

Quantum games with correlated noise

Simulation of continuous variable quantum games without entanglement

The Rule for Evolution of Cooperation in Quantum Games

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