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

I suppose that  you probably think of a procedure like this:
1. calculate all the eigenstates of the system to an operator.
2. calculate the transition probabilities
3. choose a random number n and then
4. say at t=3Dt0 that psi:=3Dpsi(n)   =
But I wanted to know wether it is possible to simulate the process of
the-collapse-of-the-wave-function (at least in principle). This means 
that I do not calculate the eigenstates but somehow simulate the
measurement process itself. This can not be done by coupling the 
system to other particles or to the vacuum because this only leads to 
an entangled system. This is the case because the interaction is 
described using the Schroedinger-Equation but this means its unitary 
but measurement is not a unitary process. Can quantum mechanics be 
considered complete without a valid description of the measurement 
process ? 

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