In quantum optics, the second-order correlation function g(2)(τ) characterizes the photon statistics of a state of light and can be used to distinguish between its classical or quantum nature. In this article, we study a simple setup which offers the possibility to generate quantum states of light with very small g(2)(0), a signature of strong anti-bunched light. This can be achieved by mixing on a beamsplitter a coherent state with a nonclassical state, such as a squeezed state, and even with a bunched state (g(2)(0) > 1) such as a Schrödinger cat state. We elucidate the interference mechanism generating such strong anti-bunching and relate it to the unconventional photon blockade. We also detail how this effect can be applied to detect weakly squeezed states of light.