Analysis of the Effect of Entanglement Operators and the Scalability of Players’ Payoff Computation in N-Player Quantum Games

Entanglement is one of the most vital resources in quantum computing. Particularly, in quantum game theory, entanglement holds significant importance since it defines the interactions and the information exchange between two or more players. In this research work, a new set of entanglement operators is introduced for N-player quantum games. This study explores how their application affects each player's behavior throughout the game. Furthermore, the entangling capabilities are tested and evaluated for a wide range of entanglement operator angles, by exploiting the Von Neumann entropy metric, both on a simulator and on a real IBM Quantum system. Their hardware efficiency, against state-of-the-art quantum games entanglement operators, is assessed in terms of circuit depths and fidelity, and showcases their great potential as multiplayer quantum games operators. Finally, three methods are compared for computing the players’ payoffs, regarding their scalability and efficiency. This study shows that in all payoff cases, the quantum game results, computed by the quantum hardware, are in accordance with the simulated ones.