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Adiabatic quantum games and phase-transition-like behavior between optimal strategies

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Abstract

In this paper we propose a game of a single qubit whose strategies can be implemented adiabatically. In addition, we show how to implement the strategies of a quantum game through controlled adiabatic evolutions, where we analyze the payment of a quantum player for various situations of interest: (1) when the players receive distinct payments, (2) when the initial state is an arbitrary superposition, and (3) when the device that implements the strategy is inefficient. Through a graphical analysis, it is possible to notice that the curves that represent the gains of the players present a behavior similar to the curves that give rise to a phase transition in thermodynamics. These transitions are associated with optimal strategy changes and occur in the absence of entanglement and interaction between the players.

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Acknowledgements

A.C.S. acknowledges financial support from the Brazilian agencies CNPq and the Brazilian National Institute of Science and Technology for Quantum Information (INCT-IQ), and M. A. P. would like to thank God for the opportunity to do this work.

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Authors and Affiliations

  1. Universidade Estadual Paulista (UNESP), Campus Experimental de Itapeva, Itapeva, São Paulo, 18409-010, Brazil

    M. A. de Ponte

  2. Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Gragoatá, Niterói, Rio de Janeiro, 24210-346, Brazil

    Alan C. Santos

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Correspondence to M. A. de Ponte.

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de Ponte, M.A., Santos, A.C. Adiabatic quantum games and phase-transition-like behavior between optimal strategies. Quantum Inf Process 17, 149 (2018). https://doi.org/10.1007/s11128-018-1918-6

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