Avishai, Y. (2012) Some Topics in Quantum Games. MA Thesis in Economics, Ben Gurion University, Beersheba, 96 p. arXiv:1306.0284. (Submitted on August 2012 to the Faculty of Social Science and Humanities at the Ben Gurion University).

has been cited by the following article:

• TITLE: Constructing Entanglers in 2-Players–N-Strategies Quantum Game

  AUTHORS: Yshai Avishai

  KEYWORDS: Quantum Games, Qubits, Qutrits, quNits, Controlled Entanglement, von Neumann Entropy

  JOURNAL NAME: Journal of Quantum Information Science, Vol.5 No.1, March 25, 2015

  ABSTRACT: 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.