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My main three questions are: 1.) What is the physical phenomenon that occurs in the interaction between a beam of light and a beam splitter that results in two beams of specific proportions of the incoming beam? 2.) How do we know that beam splitters split only the incoming beam and not its constituent photons (I'm assuming that it is because we observe no change in the light's frequency before and after the beam splitter)? 3.) How do beam splitters reliably split beams into specific proportions of the incoming beam (50/50, for example) while also giving the exiting photons a superposed (uncertain?) state of which output beam they (each individual photon) are in?

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If we send a single photon at a beam splitter, and then put sensors on the outputs, we always observe a single photon, never two. Each photon sent through the beam splitter gets put into a superposition state. There are many different kinds of superposition state. The space of all possible superpositions for a single qbit is equivalent to a sphere, with pure states on the surface and mixed states in the interior. If a single photon is sent at a beam splitter, the result is always a pure state. Which pure state depends on the thickness of the silvering.

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