Significance of entangling operators in the purview of modified EWL scheme

Recently, a modified approach to Eisert, Wilkens and Lewenstein quantization scheme has been proposed in Vijayakrishnan and Balakrishnan (Quantum Inf Process 18:112, 2019), with an aim to explore the two-qubit entangling operators in the domain of game theory. In the present work, we show the implications of such a modification by considering the possibility of conversion of symmetric to potential game, when one of the players uses a quantum strategy while the other resorts to classical strategy. Secondly, we show that entangling operators which produce same average payoffs do not produce same average entanglement. Furthermore, the converse is also found to hold good. Following which, we show that conversion of symmetric to potential games can be done through operators which are perfect entanglers.