Significance of Entangling Operators in Quantum Two Penny Flip Game

For every rule of a single penny flip game, there exists a unitary operation as a winning strategy for a quantum player. Now, in the two penny flip game, an extra option is available, viz. the use of entangling operators. However, it is known that entangling operators are not useful in this case, and a tensor product of unitary operators works just fine. In this work, we look for the significance of the entangling operators, if any, under the situation that the options available to the classical player are expanded. We extend the problem to a more general case and it is shown that there is no entangling operator capable of guaranteeing the victory of the quantum player. Eventually, we reach the classical game situation in a quantum setup of a game.