The paper deals with the synchronization of a new statistically highly performant function firstly introduced by Lozi. The synchronization is reached via observers which reconstruct all the states of the original system, using only a partial information of it. The map has been rewritten as a piece-wise affine one, which allows to design two types of observers: an exact (dead-beat) observer, and an asymptotic observer. Both observers have been analysed and compared; the dead-beat observer guarantees an exact convergence; however, synchronization can not be preserved in an autonomous regime (if the observer is switched off), because the map is highly chaotic, and the trajectories diverge due to the finite computer precision. The asymptotic observer is more robust in case of noise, but the convergence is slower, and the error converges to zero only asymptotically. In the latter case, several observers have to run in parallel, and the criteria to select the converging one are derived