  Various model-independent aspects of the $\bar{K} N \to K \Xi$ reaction are
investigated, starting from the determination of the most general structure of
the reaction amplitude for $\Xi$ baryons with $J^P=\frac12^\pm$ and
$\frac32^\pm$ and the observables that allow a complete determination of these
amplitudes. Polarization observables are constructed in terms of spin-density
matrix elements. Reflection symmetry about the reaction plane is exploited, in
particular, to determine the parity of the produced $\Xi$ in a
model-independent way. In addition, extending the work of Biagi
$\mathrm{\textit{et al. } [Z. Phys.\ C \textbf{34}, 175 (1987)]}$, a way is
presented of determining simultaneously the spin and parity of the ground state
of $\Xi$ baryon as well as those of the excited $\Xi$ states.
