This report presents a first attempt to introduce noise into the protocol of reference-frame- independent quantum key distribution. It is found that a frequently accepted manner to introduce noise,...Show moreThis report presents a first attempt to introduce noise into the protocol of reference-frame- independent quantum key distribution. It is found that a frequently accepted manner to introduce noise, according to the model of Eckert et al. proposed in ref. [1] leads to non-physical state matrices and therefore another model is proposed: the $\beta_{\pi}$-noise model. In this model the basis states composing the state matrix are perturbed by a complex quantity. For pure states this approach is applied to all state matrix elements, whereas for mixed states it is applied only to the diagonal elements. The off-diagonal elements in the mixed state are perturbed by a complex quantity that is independent of the perturbations on the basis states that the matrix element consists of. Using a Monte Carlo simulation, statistics on the quantum bit error rate as well as the transverse correlation factor are obtained for this model. However, although the $\beta_{\pi}$-noise model solves the main issues that lead to the conclusion that the model of Eckert et al. might infer non-physical state matrices, it does not yet guarantee the state matrix is always physical: a mixed state may still violate positive semi-definiteness. Therefore the original model is improved by perturbing all basis states as before and using this approach for all state matrix elements. In this improved version of the $\beta_{\pi}$-noise model Eve is present as a (complex) scaling of the off-diagonal state matrix elements. Thus, positive semi-definiteness is guaranteed for this noise model. Also for this improved version of the model statistics on the quantum bit error rate and the transverse correlation factor are presented, thereby describing the implications on an experiment.Show less
