Internal trace for detector variables and the quantum theory of measurement

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Abstract
The wave-packet reduction in quantum measurements is investigated for quantum-mechanical treatments except for the macroscopic limit in the final step. We show that the internal trace represented by the integrations over the internal variables of detectors, which are independent of the measured physical quantity, leads to the disappearance of the interference in the density matrix and then a reduction of the wave packet. Through the evaluations of two simple examples we clarify the role of the internal trace in quantum measurements and point out the difference between our idea and the others.