Game Theory Based View to the Quantum Key Distribution BB84 Protocol

Quantum key distribution uses quantum mechanics to guarantee secure communication. BB84 is a widely used quantum key distribution that provides a way for two parties, a sender, Alice, and a receiver, Bob, to share an unconditionally secure key in the presence of an eavesdropper, Eve. In a new approach, we view this protocol as a three player static game in which Alice and Bob are two cooperative players and Eve is a competitive one. In our game model Alice´s and Bob´s objective is to maximize the probability of detecting Eve, while Eve´s objective is to minimize this probability. Using this model we show how game theory can be used to find the strategies for Alice, Bob and Eve.