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The following diagram is from Experimental Realization of a Quantum Autoencoder: The Compression of Qutrits via Machine Learning enter image description here

How this setup works:

What will be obtained from this set up is the state vector of the input light (I don't use the term 'photon' because it might not be necessary) just before entering stage (c) and its state vector when exiting stage (c). Due to the |H> |V> two different polarization states and two different optical paths (upper one and lower one), there are three bases states (notice that this beam displacer only deflects |v> polarized light so not four bases), so its state vector is 3-dimensional at the input of (c) and is expected to be 2-dimensional at the output of (c) because the autoencoder part is supposed to compress the state vector such that the upper path basis is always 0 valued.

My question is, why is it necessary to use single photon for this experiment?

In order to distinguish the statistics of different state vectors, I can just use something to measure the intensity of the output light at the two optical path; specifically for the lower path at output, I use another beam displacer to separate V and H light and measure their intensities separately. With knowing those intensities, I can get the coefficients of each basis and hence known exactly the state vector, or can I?

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    $\begingroup$ are you asking "why are single photons important for quantum computing" or "why are single photons necessary for this quantum autoencoder protocol"? These are very different questions $\endgroup$ – glS Mar 15 at 17:34
  • $\begingroup$ @gIS Both actually. Are you implying in this particular case it is not necessary but in general it is needed for some other reason? $\endgroup$ – Zzy1130 Mar 17 at 5:38
  • $\begingroup$ no I'm saying that they are completely different questions. Whether single photons are "important" for quantum computing in general is somewhat ill-posed: what do you mean with "important"? They are useful, as in they can be used for quantum computing. This is unrelated to whether it is necessary to use single photons for this particular implementation. You should focus the post to ask one of the two questions, otherwise it's too broad $\endgroup$ – glS Mar 17 at 7:12
  • $\begingroup$ @gIS okay I've modified my question a bit to just focus on this particular implementation. $\endgroup$ – Zzy1130 Mar 17 at 8:49
  • $\begingroup$ the title remains at odds with what is actually been asked in the body of the question. I edited the title assuming that you meant to ask the question in the body. Feel free to revert the edit (and then also clarify the question) if that's not the case. I'm still not sure whether you are asking specifically about the use of single-photon sources, or just about the use of single photons. Single photon sources are necessary if you want to use single photons. The use of single photons is most likely not a necessary feature of this protocol (I admit I haven't read the paper though) $\endgroup$ – glS Mar 17 at 9:04

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