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The well known no-clone theorem states that it is impossible to exactly copy the quantum state of a system. The explanation seems to reside in the uncertainty principle...

But, for example, if we measure a photon with known polarization (say vertical) with a vertical linear polarizer we obtain a vertically polarized photon as output. Wouldn't that be an example of copying the original photon since the measurement result isa photon with equal polarization as the incoming photon (i.e. a copy of the incoming one)? Where is the flaw in my thinking?

Thanks!

Fog37