  This work illustrates a possible application of quantum game theory to the
area of quantum information, in particular to quantum cryptography. The study
proposed two quantum key-distribution (QKD) protocols based on the quantum
version of the Monty Hall game devised by Flitney and Abbott. Unlike most QKD
protocols, in which the bits from which the key is going to be extracted are
encoded in a basis choice (as in BB84), these are encoded in an operation
choice. The first proposed protocol uses qutrits to describe the state of the
system and the same game operators proposed by Flitney and Abbott. The
motivation behind the second proposal is to simplify a possible physical
implementation by adapting the formalism of the qutrit protocol to use qubits
and simple logical quantum gates. In both protocols, the security relies on the
violation of a Bell-type inequality, for two qutrits and for six qubits in each
case. Results show a higher ratio of violation than the E91 protocol.
