Re: Can decoherence (reduction to an eigenstate) be simulated with a computer ?

    This question goes to the heart of the interpretation of quantum
mechanics (that is, what does quantum mechanics mean). There are many
answers to this question, and an enormous amount of discussion; the reason
for this is that questions of interpretation are metaphysical, and cannot
be answered by experiment.

    Can you simulate the measurement process itself? Yes, but not without
introducing assumptions about it. Will the result of your simulation tell
you anything that you didn't introduce through your assumptions (either
deliberately or inadvertantly)? No, I don't believe that it will.

    Can quantum mechanics be considered a complete theory without a
description of the measurement process? This is a question of philosoply
more than physics, and whether one answers yes or no depends on how one
defines a complete theory.
Indeed, whether or not the wave function collapses is basically a matter of
interpretation rather than something that can be measured directly (it is
clear that after a measurement the system has a different set of
expectation values, but how you interpret that is exactly that - an
interpretation).

    There is a wealth of literature on this subject; a good starting point
(even though it is incomplete) is the Measurement in quantum mechanics FAQ,
which can be found at 
http://www.mtnmath.com/faq/meas-qm.html#toc12 . It contains many
references. Personally, I find the discussion in Park's "Introduction to
the Quantum Theory" (3rd edition, McGraw-Hill 1992) to be particularly
lucid (it is Chapter 10 in this edition).