  The BESIII collaboration has recently reported the first time measurement of
the decay asymmetry $\alpha(\Lambda_c^+ \to \Xi^0 K^+) = 0.01 \pm 0.16(stat.)
\pm 0.03(syst.)$ and also a sizable phase shift of $\delta_P-\delta_S = -1.55
\pm 0.25$ or $1.59\pm 0.25$ between S- and P-wave amplitudes. This implies
significant strong phase shifts in the decay amplitudes. The strong phases
indicate the existence of rescattering or loop effects, which are challenging
to calculate due to non-perturbative effects. By employing the flavor $SU(3)_F$
symmetry and applying the K\"orner-Pati-Woo theorem to reduce the number of
parameters, we find that the current data already allow us to obtain, for the
first time, model-independent decay amplitudes and their strong phases. The
establishment of the existence of sizable strong phases opens a window for
future investigations into CP violation. In our fit, a notable discrepancy
emerges in the branching ratio of $\Xi_c^0 \to \Xi^- \pi^+$. The direct
relationship between $\Gamma (\Lambda_c^+ \to \Lambda e^+\nu_e)$ and $\Gamma
(\Xi_c^0 \to \Xi^- e^+\nu_e)$, along with newly discovered $SU(3)_F$ relations,
collectively suggests an underestimation of $\mathcal{B}(\Xi_c^0 \to \Xi^-
\pi^+)$ in experimental findings.
