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### 3. Fuzzy projections

For each let be the fuzzy projection opearator defined by the formula:
 (11)

where ), or better: is a parameter that measures the "fuzziness." The extreme cases are not the very interesting ones: for we get the identity operator - maximal fuzziness and no information whatsoever, while for we get the sharp projection

We restrict the range of the parameter to the interval because only in this range is a positive operator. It is easy to see that this is so. Indeed, a Hermitian matrix is positive when its eigenvalues are positive, and the eigenvalues of are thus On the other hand negative for is the same as positive for thus we restrict the range of to

It is the operators that will act on quantum states to implement "quantum jumps" whenever detectors "flip."

The overall coefficient in the definition (), chosen to be here, is not important because in applications each of the operators is multiplied by a coupling constant, and, in our case, when we are not interested in timing of the jumps, the value of the coupling constant plays no role.

Next: 4. Jumps are implemented Up: 2. The algorithm Previous: 2. Spin directions

2002-04-11