$\mathrm{CP}$-Violating Interference Effects in Radiative $K^0$ Decays

It is shown that the observation of interference between $K_L$ and $K_S$ decays in the partial decay rate into any nonleptonic mode is direct evidence of $\mathrm{CP}$ violation. The examples of $K^0\to \gamma +\gamma$ and $K^0\to {\pi }^{+}+{\pi }^{-}+\gamma$ are analyzed in detail; a large interference effect may be possible in either of these cases if there is a large $\mathrm{CP}$ violation associated with interactions involving photon emission.