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Quantum Two Player Game in Thermal Environment.

Dajka J, Kłoda D, Łobejko M, Sładkowski J - PLoS ONE (2015)

Bottom Line: A two-player quantum game is considered in the presence of thermal decoherence.It is shown how the thermal environment modeled in terms of rigorous Davies approach affects payoffs of the players.The general considerations are exemplified by the quantum version of Prisoner Dilemma.

View Article: PubMed Central - PubMed

Affiliation: Institute of Physics, University of Silesia, Katowice, Poland; Silesian Center for Education and Interdisciplinary Research, University of Silesia, Chorzów, Poland.

ABSTRACT
A two-player quantum game is considered in the presence of thermal decoherence. It is shown how the thermal environment modeled in terms of rigorous Davies approach affects payoffs of the players. The conditions for either beneficial or pernicious effect of decoherence are identified. The general considerations are exemplified by the quantum version of Prisoner Dilemma.

No MeSH data available.


Related in: MedlinePlus

Payoff differences Eq (29) taken at different time instances t for Alice–Bob strategy profile (𝓘,𝓘U) with the quantum strategy Eq (12) with U = U(π/2,0, π/2).The thermal Davies environment (with A = 2G = 2) influences only one player (either Bob or Alice) and p = 0. The contours denote the border between positive and negative payoff difference.
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pone.0134916.g001: Payoff differences Eq (29) taken at different time instances t for Alice–Bob strategy profile (𝓘,𝓘U) with the quantum strategy Eq (12) with U = U(π/2,0, π/2).The thermal Davies environment (with A = 2G = 2) influences only one player (either Bob or Alice) and p = 0. The contours denote the border between positive and negative payoff difference.

Mentions: First we consider (𝓘,𝓘U) strategy profile. The payoff differences Eqs (31 and 30) calculated at different time instants are presented in Fig (1). The quantum part of the Bob’s strategy is chosen to be U = U(π/2,0, π/2). The payoff difference Δ$ can be either positive (Bob is winning) or negative depending on the value of γ. This dependence is strongly affected by thermal environment. Moreover, this dependence is very different in the case when the environment is attached either to Bob’s or Alice’s qubit. Let us notice that in the case when thermal environment affects Bob’ qubit his payoff is in the long time limit always larger than the payoff of Alice i.e. Δ$B > 0 for all γ. It is not the case when the noisy qubit belongs to Alice. There is a range of γ when Δ$A < 0 i.e. when $B < $A. In other words, in the situation when Alice can control or choose γ and possesses noisy qubit is favorable if she tries to win or at least minimize her losses. Let us also notice that there are parameters γ < π/4 such that Δ$A > Δ$B > Δ$ and, simultaneously Δ$ < 0. This range of parameters is particularly favorable for Bob who wins due to the presence of thermal environment.


Quantum Two Player Game in Thermal Environment.

Dajka J, Kłoda D, Łobejko M, Sładkowski J - PLoS ONE (2015)

Payoff differences Eq (29) taken at different time instances t for Alice–Bob strategy profile (𝓘,𝓘U) with the quantum strategy Eq (12) with U = U(π/2,0, π/2).The thermal Davies environment (with A = 2G = 2) influences only one player (either Bob or Alice) and p = 0. The contours denote the border between positive and negative payoff difference.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4556192&req=5

pone.0134916.g001: Payoff differences Eq (29) taken at different time instances t for Alice–Bob strategy profile (𝓘,𝓘U) with the quantum strategy Eq (12) with U = U(π/2,0, π/2).The thermal Davies environment (with A = 2G = 2) influences only one player (either Bob or Alice) and p = 0. The contours denote the border between positive and negative payoff difference.
Mentions: First we consider (𝓘,𝓘U) strategy profile. The payoff differences Eqs (31 and 30) calculated at different time instants are presented in Fig (1). The quantum part of the Bob’s strategy is chosen to be U = U(π/2,0, π/2). The payoff difference Δ$ can be either positive (Bob is winning) or negative depending on the value of γ. This dependence is strongly affected by thermal environment. Moreover, this dependence is very different in the case when the environment is attached either to Bob’s or Alice’s qubit. Let us notice that in the case when thermal environment affects Bob’ qubit his payoff is in the long time limit always larger than the payoff of Alice i.e. Δ$B > 0 for all γ. It is not the case when the noisy qubit belongs to Alice. There is a range of γ when Δ$A < 0 i.e. when $B < $A. In other words, in the situation when Alice can control or choose γ and possesses noisy qubit is favorable if she tries to win or at least minimize her losses. Let us also notice that there are parameters γ < π/4 such that Δ$A > Δ$B > Δ$ and, simultaneously Δ$ < 0. This range of parameters is particularly favorable for Bob who wins due to the presence of thermal environment.

Bottom Line: A two-player quantum game is considered in the presence of thermal decoherence.It is shown how the thermal environment modeled in terms of rigorous Davies approach affects payoffs of the players.The general considerations are exemplified by the quantum version of Prisoner Dilemma.

View Article: PubMed Central - PubMed

Affiliation: Institute of Physics, University of Silesia, Katowice, Poland; Silesian Center for Education and Interdisciplinary Research, University of Silesia, Chorzów, Poland.

ABSTRACT
A two-player quantum game is considered in the presence of thermal decoherence. It is shown how the thermal environment modeled in terms of rigorous Davies approach affects payoffs of the players. The conditions for either beneficial or pernicious effect of decoherence are identified. The general considerations are exemplified by the quantum version of Prisoner Dilemma.

No MeSH data available.


Related in: MedlinePlus