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Quantum prisoners’ dilemma under enhanced interrogation

  • George Siopsis
  • Radhakrishnan Balu
  • Neal Solmeyer
Article

Abstract

In the quantum version of prisoners’ dilemma, each prisoner is equipped with a single qubit that the interrogator can entangle. We enlarge the available Hilbert space by introducing a third qubit that the interrogator can entangle with the other two. We discuss an enhanced interrogation technique based on tripartite entanglement and analyze Nash equilibria. We show that for tripartite entanglement approaching a W-state, we calculate the Nash equilibria numerically and show that they coincide with the Pareto-optimal choice where both prisoners cooperate. Upon continuous variation between a W-state and a pure bipartite entangled state, the game is shown to have a surprisingly rich structure. The role of bipartite and tripartite entanglement is explored to explain that structure. As an application, we consider an evolutionary game based on our quantum game with a network of agents on a square lattice with periodic boundary conditions and show that the strategy corresponding to Nash equilibrium completely dominates without placing any restrictions on the initial set of strategies.

Keywords

Quantum games Nash equilibrium Pareto-optimal Entanglement Quantum circuit 

Notes

Acknowledgements

We wish to thank the anonymous reviewer for the suggestion of discussing an application of our game.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics and AstronomyThe University of TennesseeKnoxvilleUSA
  2. 2.Computer and Information Sciences Directorate, Army Research LaboratoryAdelphiUSA
  3. 3.Computer Science and Electrical EngineeringUniversity of Maryland Baltimore CountyBaltimoreUSA
  4. 4.Sensors and Electron Devices Directorate, Army Research LaboratoryAdelphiUSA

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