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Quantum prisoners’ dilemma under enhanced interrogation

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN, 37996-1200, USA

    George Siopsis

  2. Computer and Information Sciences Directorate, Army Research Laboratory, Adelphi, MD, 21005-5069, USA

    Radhakrishnan Balu

  3. Computer Science and Electrical Engineering, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA

    Radhakrishnan Balu

  4. Sensors and Electron Devices Directorate, Army Research Laboratory, Adelphi, MD, 21005-5069, USA

    Neal Solmeyer

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  1. George Siopsis
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  2. Radhakrishnan Balu
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  3. Neal Solmeyer
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Correspondence to George Siopsis.

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Siopsis, G., Balu, R. & Solmeyer, N. Quantum prisoners’ dilemma under enhanced interrogation. Quantum Inf Process 17, 144 (2018). https://doi.org/10.1007/s11128-018-1915-9

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