Does diffraction (prism) conserve photon number? I have read these questions:
Why do prisms work (why is refraction frequency dependent)?
Single Photon though prism
Does a single white photon exist?

There are lasers that emit "supercontinuum" beams, in intense pulses. A pulse is very short, on the order of a femtosecond or less. One of the pulses, passed through a diffraction grating, fans out into an array of beams of different wavelength / frequency. Downstream, the beams can be recombined coherently to form a new pulse. This is an interferometer of sorts- a temporal interferometer.
  Now we need an experiment that produces a particular result if and only if (A) only one photon passes through the system at a time, and (b) the photon must have had multiple wavelengths.


Now based on these answers, there can exist a single photon which is in a superposition of frequencies, that we could call white.
There exist single photon Quantum Dot sources, and we might be able to produce a photon of that kind.
If we let that photon through a prism, the outcoming photon could either be a single photon still in a superposition, or the diffraction could actually separate (downconversion or multiple photon emission) the photon into separate photons with different wavelengths? Would we see at the detector a single photon of random wavelength, or all the photons that build the white color?
Question:


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*Does diffraction (prism) conserve photon number?

 A: The third link in your question was answered by anna v as follows:

As a quantum mechanical entity photons can be in superposition, and three of them with appropriate frequencies might fall in the group that gives the perceptiong of white in the diagram . There is no "white frequency", as color perception is a biological mechanism.

From their emission to their absorption, photons have an energy content that does not change under any circumstances. If a photon leaves the prism at a lower frequency, you can be sure that an incoming photon has been absorbed, and what we see is a re-emitted photon (plus lost energy dissipated by the prism). The sketch in the question is a good illustration to the question but not a realistic scenario.

Does diffraction (prism) conserve photon number?

Good question for further research.
On the first glance the answer is yes. Prism is made form glas. Behind glas windows we see the world in the same colors as without the window. When you think about it, doubts come up. Are the colors behind a 1 meter thick glas really the same as without?
It turns out that photons even in glas interact (some of them or all?, sometimes or always?) If absorption and re-emission processes are taking place in a prism (that is why a mentioned further research of the photon-glass-interactions), the number of photons is not conserved. The remaining energy from slightly shifted to the red re-emitted photons heats the prism and leaves the prism in the form of infrared photons.
In Short. No interactions without energy losses. The photon number is not conserved.
