Does the transmitted part of the light possess a certain property that leads to being transmitted? Has the beam splitter prepared light with the property "is being transmitted"? The question can be answered using the general scheme of preparation and test. To this end, a second beam splitter is set in the way of the transmitted beam. This second beam splitter performs the test measurement. If the light in the transmitted beam has the property "is being transmitted" it must show in the test measurement. Thus at the second beam splitter, all the light would pass through, nothing would be reflected.
The result of the experiment shows that the transmitted beam did not
possess the property "is being transmitted". A beam splitter does not perform
such a preparation. In fact, it is not possible at all to prepare a beam
of light in such a way that it totally passes through a half-silvered mirror.