Adiabatic quantum games and phase-transition-like behavior between optimal strategies - de Ponte, M. A. [UNESP]; Santos, Alan C. (Springer Nature, 2018)
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.
Keywords: Adiabatic evolution; Phase-transition-like behavior; Quantum games