Wednesday, January 29, 2020

quantum mechanics - Stimulated emission and No cloning theorem


I have a little trouble with the simulated emission. I know of the no-cloning theorem which states that it is not possible to duplicate any state.


One the other hand, I know about the stimulated emission which out of a photon produce exactly the same (wavelength, polarisation, etc...). Maybe the fact is that the excited atom do a measure. (Let's say it can stimulate emission with only one direction of polarisation.)


But now if I have a statiscal number of atoms with random "polarisation" direction, I should be able to copy any incident photon. I've made a cloning machine.


This cannot be true because of the no-cloning theorem. But I can't figure why.



Answer



Sure you can clone a state. If you know how to produce it, you can just produce one more copy.



The answer to your question therefore lies in the specifics of the no-cloning theorem. It states that it is not possible to build a machine that clones an arbitrary (previously unknown!) state faithfully.


Stimulated emission does not fulfill this. Given an atom, only a certain range of frequencies, etc. can actually be used to produce stimulated emission, so you can't faithfully clone an arbitrary state. It's just an approximation to cloning, which is not prohibited.


See also: http://arxiv.org/abs/quant-ph/0205149 and references therein.


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