Nonlocal correlations and noise in different settings of a two-player game

Nonlocal correlations in a quantum mechanical system hold an indispensable place in understanding the foundational aspects of theory, and for exploring efficient theoretical and experimental proposals in the regime of quantum computation and information which are otherwise not possible using classical resources. One of the possible ways to understand the nuances of nonlocal correlations is to put it in the framework of game theory. For this purpose, we address the issue of decoherence and protection of nonlocal correlations from local noise from the perspective of a game, considering the two players as noise and weak measurement reversal operations, respectively. In order to effectively understand the moves of players, we study maximum payoff and Nash equilibrium strategies for different noisy channels. Our results compare two different situations where payoffs of players are defined using the Bell inequality and discord, respectively. The analysis shows a contrasting description of payoffs and strategies in two different cases. We believe that the results obtained here will help one to understand the intricacies involved in the process of entanglement distribution through noisy channels, evaluating optimal parameters to obtain maximum payoff in the designed game, and Nash equilibrium strategies of players to win the desired game.