Exploring the impact of spontaneous emission in two quantum game-based key-distribution protocols

Abstract

In this work, we investigate the influence that spontaneous emission has on the performance and security of both a qubit and a qutrit quantum key distribution protocols, if these were to be implemented using two- and three-level atoms, respectively. These protocols were developed based on the mechanics of a quantum version of the Monty-Hall game. In the case of three-level atoms, the three possible configurations (V, Ξ, Λ) are considered. In both protocols, an additional step, consisting on discarding some specific non-valid cases, is found to reduce the bit error ratio (BER). Regarding the security of the protocols, we are able to define secure regions, dependent on the spontaneous emission parameters, within which the protocols are deemed secure due to the violation of Bell-type inequalities. Furthermore, our results show that the choice of three-level atom configuration significantly impacts the protocol performance. We are able to determine that the Λ configuration provides a lower BER than the V and Ξ configurations within their respective secure regions.