Quantum Non-Local Games

This work investigates upon the idea of using quantum entanglement in reference to non-local(NL) games. We begin with the definition of a non-local game and study it’s importance in context to the advantage gained over playing the game classically i.e. when no entanglement is involved. For certain NL games, like the XOR games, the gap between the value of the game(maximum success probability) played classically and other using entanglement sharing,can be computed efficiently. But for a general class of NL games, while determining the classical value of the game is NP-Hard, the problem of computing the quantum value is not known to be decidable. Even deciding whether there is a perfect quantum strategy is not known to be decidable. We consider a special class of NL games, namely the Binary Constraint System(BCS) games, and look whether they admit a perfect strategy or not. Next, we take a BCS game and give a quantum strategy which has a success probability higher than that of the classical value of that game.