  The study of non-Abelian Majorana zero modes advances our understanding of
the fundamental physics in quantum matter, and pushes the potential
applications of such exotic states to topological quantum computation. It has
been shown that in two-dimensional (2D) and 1D chiral superconductors, the
isolated Majorana fermions obey non-Abelian statistics. However, Majorana modes
in a $Z_2$ time-reversal invariant (TRI) topological superconductor come in
pairs due to Kramers' theorem. Therefore, braiding operations in TRI
superconductors always exchange two pairs of Majoranas. In this work, we show
interestingly that, due to the protection of time-reversal symmetry,
non-Abelian statistics can be obtained in 1D TRI topological superconductors
and may have advantages in applying to topological quantum computation.
Furthermore, we unveil an intriguing phenomenon in the Josephson effect, that
the periodicity of Josephson currents depends on the fermion parity of the
superconducting state. This effect provides direct measurements of the
topological qubit states in such 1D TRI superconductors.
