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While a beam splitter can be thought of as producing a unitary transformation on the input states, it also known that in a realistic beam splitter, the reflective layer sandwiched between the two triangular prisms can absorb some of the incident photons.So, it appears that although a beam splitter effects a unitary transformation, it does have some chance of acting as a photon detector(A measurement appparatus). The question is this: Is this chance associated with manufacturing imperfections(so that it could be eliminated in principle) or is this chance irreducible and associated with the quantum in-determinism?

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Manufacturing. The laws of quantum physics don't exclude a perfect unitary transformation. Of course, any real device will have finite losses.

(On a different note, I would not call this "measurement" - there is no information obtained. It is rather decoherence.)

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  • $\begingroup$ But, why not consider that to be a measurement? If the beam splitter is placed at a particular spatial region and if the coating happen to absorb a photon, is the situation not alike the case where a photon impinges on a photographic plate? i.e Does this situation not count as a position measurement? $\endgroup$ May 10, 2020 at 20:58
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    $\begingroup$ @VarunImmanuel If you want to call it a measurement, call it a measurement. But how do you know that a photon got measured? It's like I am doing the measurement and refusing to tell you the result. $\endgroup$ May 10, 2020 at 21:58
  • $\begingroup$ this is a sketchy position measurement method I have in mind: If a photon got absorbed by the reflective layer of the beam splitter at a particular spot, perhaps the temperature of the material in the immediate neighborhood of that spot gets warmer relative to the other regions of the coating. Before dissipation occurs, we imagine dismantling the beam splitter to find out which point on the coated surface (which is now the base of one of the cutout triangular prisms) , the warming happened. Does this not count as a valid method ? $\endgroup$ May 30, 2020 at 1:19

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