  We suggest an optical method which tests a nonclassical feature with a
coherent state input. The test is designed with a multiplexer of on/off
detectors and post-selection, adopting sub-binomiality as a nonclassical
feature, replacing Mandel's $Q$-factor. The sub-binomiality is shown negative
even for coherent states when the post-selection is made. However, we show that
it can be reproduced also by a classical model assuming a stochastic on/off
detectors. In the sense, the sub-binomiality is unlikely to identify the
genuine nonclassicality. On the other hand, we propose a coincident probability
of first two branches of the multiplexer and show that the classical model
fails to reproduce the quantum coincident probability. The failure of the
classical model results from the classical description of light, i.e. the
divisibility of intensity into parts no matter how small it is. Then our
optical test identifies a nonclassical feature of coherent states against the
classical divisibility of light, which we call irreducibility.
