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Variable entangling in a quantum prisoner’s dilemma cellular automaton

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Abstract

The effect of variable entangling on the dynamics of a spatial quantum formulation of the iterated prisoner’s dilemma game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The effect of spatial structure is assessed when allowing the players to adopt quantum and classical strategies, both in the two- and three-parameter strategy spaces.

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Notes

  1. Cellular automata are spatially extended dynamical systems that are discrete in all their constitutional components: space, time and state-variable. Uniform, local and synchronous interactions, as assumed here, are landmark features of CA [34].

  2. Provided that \(P-S \le \mathfrak {T}-R\), the critical values are to be: \(\gamma ^*= \arcsin \big (\sqrt{\displaystyle \frac{P-S}{\mathfrak {T}-S}}\big )\), and \(\gamma ^+= \arcsin \big (\sqrt{\displaystyle \frac{\mathfrak {T}-R}{\mathfrak {T}-S}}\big )\). Thus, (0.524,0.785) with the (5,3,2,1)-PD parameters, and \(\gamma ^*=\gamma ^+=0.616\) with the (4,3,2,1)-PD parameters.

  3. The reference [14] is also relevant in this respect, but the occasional reader should be warned about the variation of the \(\alpha \) and \(\beta \) parameters in the \([-\pi ,\pi ]\) interval instead of in \([0,\pi /2]\), as proposed for \(\alpha \) in the seminal EWL paper.

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Acknowledgments

This work was supported by the Spanish Grant M2012-39101-C02-01. Part of the computations of this work were performed in EOLO and FISWULF, HPC machines of the International Campus of Excellence of Moncloa, funded by the Spanish Government and Feder Funds.

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  1. ETSIA (Estadística, GSC), Technical University of Madrid, C.Universitaria, 28040, Madrid, Spain

    Ramón Alonso-Sanz

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Correspondence to Ramón Alonso-Sanz.

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Alonso-Sanz, R. Variable entangling in a quantum prisoner’s dilemma cellular automaton. Quantum Inf Process 14, 147–164 (2015). https://doi.org/10.1007/s11128-014-0834-7

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