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The term "state preparation procedure" is widely used in quantum mechanics without clear explanation of what it is or isn't.

Sometimes it's suggested that it is a controlled procedure in a laboratory.

Sometimes wider definitions are used.

If the definition is too wide - for example it's any procedure - then it loses any value.

For example is there a state preparation procedure for:

1) Schrödinger's cat 2) a hydrogen atom 3) a photon

In your answers please would you specify the procedure and the state vector it produces.

user184773
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It's any procedure that outputs repeated examples of the same quantum system - particle or multiparticle system - in the same quantum state. That's all one can say.

Exactly how one implements the procedure is up to the ingenuity and imagination of the experimenter. One simply has to be to prove, using sound physical principles, that the output of the procedure is repeatably the same quantum state.

There are a few general tricks and ideas one uses. For example, culling a quantum mixture is a common tactic: one simply uses some kind of barrier or filter to remove all population members not in the desired quantum state. An example of this would be the use of a polarizer to pass only photons in a certain polarization into an apparatus. The Stern-Gerlach experiment is another similar example, where an electron population is sorted according to spin by an appropriately aligned magnetic field. Cooling can be another tool, forcing a population towards the unique ground state, as discussed by JoshPhysics's answer here.

Sometimes physical processes replicate a certain quantum state from a seed example, and this can be used for preparation of large populations in the same pure state. This is what happens in stimulated emission, in a laser for example. Note that such replication is not gainsaying the No Cloning Theorem, as discussed in Wataya's excellent answer here.

Selene Routley
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    Good Answer...it seems to follow that most States do not have a preparation procedure, only a few can be prepared using a repeatable procedure. Do you agree? – user184773 Feb 23 '18 at 11:14
  • @user184773 Yes, this is in fact an informal description of what the No Cloning Theorem really says. Informal as you should specify what do you mean by "most" (which you can). – Alessandro Della Corte Apr 28 '22 at 08:02