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Let us now discuss the algebraic operation that is associated with
each quantum jump. Suppose before the jump the state of the
quantum system is described by a projection operator ,
being a unit vector on the sphere. That is, suppose, before
the detector flip, the spin "has" direction . Now, suppose
the detector
flips, and the spin right after the
flip has some other direction,
. What is the relation
between and
? It is easy to see that the action
of the operator
on a quantum state vector is
given, in terms of operators, by the formula:

(12) 
where
is a positive number. It is a
simple (though somewhat lengthy) matrix computation that leads to
the following result:

(13) 

(14) 
where
denotes the scalar product

(15) 
Next: 5. Transition probabilities
Up: 2. The algorithm
Previous: 3. Fuzzy projections
20020411