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.