A Quantum Mechanical model of measurement

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I think chapter 9 of Ballentine is a good place to get introduced to this stuff.
It's good, but for some reason (unclear to me) Ballentine never mentions decoherence. For example, after Eq. (9.13) he says:
"It is clear that the nondiagonal terms in (9.13) cannot vanish so as to reduce the state to the form of (9.12) ..."
At this point nothing would be more natural than to mention that decoherence provides a FAPP mechanism to arrive at (9.12). Yet, for some reason, Ballentine does not say anything of that sort. Do you have any idea what his reasons might be?
 
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If you're concerned about what exactly the H looks like, I'm sure there are lots of toy models in the literature, but I haven't studied any of them (except for a quick look at section II in that paper...I didn't try to understand all the details).
Yes, I guess that's exactly what I'm concerned about. So I found
A. Peres, Phys Rev D. 39 3943
which at least describes the model apparatus a bit more fully. However, it is not a finite-state system, so isn't as easy to play around with it on Matlab or Octave.
I think chapter 9 of Ballentine is a good place to get introduced to this stuff
I'm glad you mentioned that. This from Ch 9 of Ballentine:
"We then introduce an interaction that produces a unique correspondence between the value of the dynamical variable and the indicator. The properties of the interaction are specified implicitly by defining the effect of the time development operator U, and since only the properties of U enter the analysis, there is no point in discussing the interaction in any more detail."
So you can see why I wanted to find out what it should look like. Admittedly, Problem 9.4 in Ballentine describes basically the same model for the apparatus as in the PRD by Peres.

So is what I've described useful at all? Since the resolution of my apparatus is arbitrary (since N can be chosen at will in the model), perhaps it provides a useful way of looking at information flow into an N-state system - I don't know.
For those who are interested, I've attached a Matlab program which implements it.
 

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