Advantage of a quantum player over a classical one in 2 × 2 quantum games

@article{Flitney2003AdvantageOA,
  title={Advantage of a quantum player over a classical one in 2 × 2 quantum games},
  author={Adrian P. Flitney and Derek Abbott},
  journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
  year={2003},
  volume={459},
  pages={2463 - 2474}
}
  • A. Flitney, D. Abbott
  • Published 24 September 2002
  • Physics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
We study a general 2 × 2 symmetric entangled quantum game. When one player has access only to classical strategies, while the other can use the full range of quantum strategies, there are ‘miracle’ moves available to the quantum player that can direct the game towards the quantum player's preferred result regardless of the classical player's strategy. The advantage pertaining to the quantum player is dependent on the degree of entanglement. Below a critical level, dependent on the pay–offs in… 
View on Royal Society
arxiv.org
91 Citations
Highly Influential Citations
1
Background Citations
20
Methods Citations
1
Results Citations
2

Figures and Tables from this paper

91 Citations

The effect of quantum noise on the restricted quantum game
It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in…
Quantum Version of a Generalized Monty Hall Game and Its Possible Applications to Quantum Secure Communications
TLDR
This work proposes a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values, and extends its quantum scheme to include multiple independent players.
A necessary and sufficient condition to play games in quantum mechanical settings
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum…
General quantum two-player games, their gate operators, and Nash equilibria
The two-players N strategies games quantized according to the EisertLewenstein-Wilkens scheme (Phys. Rev. Lett. 83 (1999), 3077) are considered. Group theoretical methods are applied to the problem…
Quantum Locality in Game Strategy
TLDR
It is shown that, for a bipartite non zero-sum game, input local quantum correlations, and separable states in particular, suffice to achieve an advantage over any strategy that uses classical resources, thus dispensing with quantum nonlocality, entanglement, or even discord between the players’ input states.
Payoffs and coherence of a quantum two-player game under noisy environment
TLDR
The results indicate that unitary strategies do not change resource measures but change players' payoffs, and entangled operator changes both, and the game symmetry is broken under noisy environment.
Payoffs and Coherence of a Quantum Two-Player Game in a Thermal Environment
TLDR
It is shown how the energy dissipation and pure decoherence affect the payoffs of the players of the (quantum version of prisoner dilemma) and the impact of the thermal environment on a coherence of game, as a quantum system, is presented.
N-Player Quantum Games in an EPR Setting
TLDR
By dispensing with the standard unitary transformations on state vectors in Hilbert space and using instead rotors and multivectors, based on Clifford’s geometric algebra, it is shown how the N-player case becomes tractable.
A quantum Chinos game with entanglement
The Chinos game is a non-cooperative game between players who try to guess the total sum of coins drawn collectively. Semiclassical and quantum versions of this game were proposed by F. Guinea and M.…
1 1 1 A ug 2 00 4 Quantum games with decoherence
A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given.…
...
...

References

SHOWING 1-10 OF 19 REFERENCES
Quantum version of the Monty Hall problem
A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game…
Entanglement playing a dominating role in quantum games
Comment on “A quantum approach to static games of complete information”
Quantum strategies
TLDR
It is proved that in general a quantum strategy is always at least as good as a classical one, and furthermore that when both players use quantum strategies there need not be any equilibrium, but if both are allowed mixed quantum strategiesthere must be.
AN INTRODUCTION TO QUANTUM GAME THEORY
TLDR
An introduction to quantum game theory is provided and the current status of the subject is reviewed.
Quantum games
Abstract In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented Eisert et al. (1999, Phys. Rev.…
Evolutionarily stable strategies in quantum games
Quantum Games and Quantum Strategies
We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also…
A quantum approach to static games of complete information
Phase-transition-like behaviour of quantum games
The discontinuous dependence of the properties of a quantum game on its entanglement has been shown to be very much like phase transitions viewed in the entanglement-payoff diagram (J Du et al 2002…
...
...