Noise effect on direction sharing protocols

There are lots of methods for sharing a direction between two parties. The methods may naturally subject to some kind of noise and it is important to study the viability of the schemes under different kinds of noises. We study the effect of local depolarizing noise on some of these protocols. By considering two protocols which encode a direction in a spins state, we show that the smaller the dimension of coding space, the less damaging will happen due to the noise. We also investigate the effect of noise on a protocol that uses quantum correlation for direction sharing and we see that by using suitable methods and enough measurements, one can overcome the noise effect.