Classical rules and quantum strategies in penny flip game

We study the quantum single penny flip game under various classical rules of the game. For every rule of the game, there exist unitary transformations which ensure the winning for quantum player. With the aim to understand the role of entangling gate for a sequential zero sum game, we extend the single penny problem to two penny problem. While entangling gates are found to be not useful, local gates are necessary and sufficient to win the game. Further, importance of one qubit operations is indicated. Various rules of two penny game is also indicated.

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