%0 Journal Article %T Constructing Entanglers in 2-Players–N-Strategies Quantum Game %A Yshai Avishai %J Journal of Quantum Information Science %P 16-23 %@ 2162-576X %D 2015 %I Scientific Research Publishing %R 10.4236/jqis.2015.51003 %X 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. %K Quantum Games %K Qubits %K Qutrits %K quNits %K Controlled Entanglement %K von Neumann Entropy %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=55019