Designing Quantum Game Strategies from Quantum Communication Protocols

Kazuo Iwama, Harumichi Nishimura, Rudy Raymond Harry Putra

Y. Avishai

In quantum games based on 2-player-N-strategies classical games, each player has a quNit (a normalized vector in an N-dimensional Hilbert space HN) upon which he applies his strategy (a matrix U∈SU(N)). The players draw their payoffs from a state . Here and J (both determined by the game’s referee) are respectively an unentangled 2-quNit (pure) state and a unitary operator such that is partially entangled. The existence of pure strategy Nash equilibrium in the quantum game is intimately related to the degree of entanglement of . Hence, it is practical to design the entangler J= J(β) to be dependent on a single real parameter β that controls the degree of entanglement of , such that its von-Neumann entropy SN(β) is continuous and obtains any value in . Designing J(β) for N=2 is quite standard. Extension to N>2 is not obvious, and here we suggest an algorithm to achieve it. Such construction provides a special quantum gate that should be a useful tool not only in quantum games but, more generally, as a special gate in manipulating quantum information protocols.

Takeshi Kawakami

Ming-Xing Luo

Omar Gustavo Zabaleta, Constancio Miguel Arizmendi

In order to analyze the power control problem, the wireless quantum network nodes are modeled as players at a quantum game. The power control problem is one of the most significant wireless communications challenges which characteristics make it proper to be modeled by means of game theory techniques. The problem results in non-cooperative game by nature, but, under quantum rules, a larger strategy space leads the players to choose a coalition strategy as the best option. Thus, the use of quantum game strategies makes possible the emergence of new equilibrium, which guarantees the best possible performance to the whole network. We show also that the whole network power consumption decreases when the intrinsic parallel behavior of quantum computation is capitalized. Moreover, the design of efficient medium access control algorithms is possible.

Vladimir G. Ivancevic, Tijana T. Ivancevic