  Due to hardware limitations, the phase shifts of the reflecting elements of
reconfigurable intelligent surfaces (RISs) need to be quantized into discrete
values. This letter aims to unveil the minimum required number of phase
quantization levels $L$ in order to achieve the full diversity order in
RIS-assisted wireless communication systems. With the aid of an upper bound of
the outage probability, we first prove that the full diversity order is
achievable provided that $L$ is not less than three. If $L=2$, on the other
hand, we prove that the achievable diversity order cannot exceed $(N+1)/2$,
where $N$ is the number of reflecting elements. This is obtained with the aid
of a lower bound of the outage probability. Therefore, we prove that the
minimum required value of $L$ to achieve the full diversity order is $L=3$.
Simulation results verify the theoretical analysis and the impact of phase
quantization levels on RIS-assisted communication systems.
