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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) as a function of temperature p calculated at a time t = 2 for Alice–Bob strategy profiles (𝓘,𝓘U) (left panel) and (𝓘,𝓕U) (right panel) with the quantum strategy Eq (12) with U = U(π/2,0, π/2).The thermal Davies environment (with G = 1) influences only one player (either Bob or Alice) and A = 2.
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pone.0134916.g004: Payoff differences Eq (29) as a function of temperature p calculated at a time t = 2 for Alice–Bob strategy profiles (𝓘,𝓘U) (left panel) and (𝓘,𝓕U) (right panel) with the quantum strategy Eq (12) with U = U(π/2,0, π/2).The thermal Davies environment (with G = 1) influences only one player (either Bob or Alice) and A = 2.

Mentions: The parameter γ is not the only one which affects Alice’s chance to win with Bob. We consider the case when the noisy qubit belongs to Alice. The energy relaxation parametrized by A is one of the parameters which most significantly affect character of thermal dissipation. As it was discussed in previous section for A = 0 (i.e. when there is only pure decoherence with no energy dissipation) Δ$A = Δ$B and the Bob’s ‘quantum benefit’ becomes neutralized. The larger A is the more different are the payoffs of Bob and Alice as presented for two strategies in Fig (3). The effect of increasing temperature is visualized in Fig (4). In the limit of high temperature Δ$A is small but positive. In other words, for some strategies and for given γ Alice defeat Bob by warming her qubit.


Quantum Two Player Game in Thermal Environment.

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

Payoff differences Eq (29) as a function of temperature p calculated at a time t = 2 for Alice–Bob strategy profiles (𝓘,𝓘U) (left panel) and (𝓘,𝓕U) (right panel) with the quantum strategy Eq (12) with U = U(π/2,0, π/2).The thermal Davies environment (with G = 1) influences only one player (either Bob or Alice) and A = 2.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0134916.g004: Payoff differences Eq (29) as a function of temperature p calculated at a time t = 2 for Alice–Bob strategy profiles (𝓘,𝓘U) (left panel) and (𝓘,𝓕U) (right panel) with the quantum strategy Eq (12) with U = U(π/2,0, π/2).The thermal Davies environment (with G = 1) influences only one player (either Bob or Alice) and A = 2.
Mentions: The parameter γ is not the only one which affects Alice’s chance to win with Bob. We consider the case when the noisy qubit belongs to Alice. The energy relaxation parametrized by A is one of the parameters which most significantly affect character of thermal dissipation. As it was discussed in previous section for A = 0 (i.e. when there is only pure decoherence with no energy dissipation) Δ$A = Δ$B and the Bob’s ‘quantum benefit’ becomes neutralized. The larger A is the more different are the payoffs of Bob and Alice as presented for two strategies in Fig (3). The effect of increasing temperature is visualized in Fig (4). In the limit of high temperature Δ$A is small but positive. In other words, for some strategies and for given γ Alice defeat Bob by warming her qubit.

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