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.
Highlights
The theory of quantum games is an evolving discipline that, similar to quantum information [1] [2], explores the implications of quantum mechanics to fields outside physics proper, such as economics, finance, auctions, gam-How to cite this paper: Avishai, Y. (2015) Constructing Entanglers in 2-Players–N-Strategies Quantum Game
One way of constructing a quantum game is to start from a standard game and to “quantize” it by formulating appropriate rules and letting the players employ quantum information tools such as qubits and quantum gates
In the present work we examine the issue of constructing J (β ) for a 2 − N quantum game based on a 2
Summary
The theory of quantum games is an evolving discipline that, similar to quantum information [1] [2], explores the implications of quantum mechanics to fields outside physics proper, such as economics, finance, auctions, gam-. One way of constructing a quantum game is to start from a standard (classical) game and to “quantize” it by formulating appropriate rules and letting the players employ quantum information tools such as qubits and quantum gates (or strategies in the quantum game nomenclature). This procedure has been applied on classical strategic games that describe an interactive decision-making in which each player chooses his strategy only once, and all choices are taken simultaneously. A simple example is a quantum game based on 2-player-2strategies classical game usually defined by a game table (for example, the prisoner dilemma).
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