Collapse of the wave function related to the use of Schmidt decomposition

In the measurement process, certain degrees of freedom of the observables are selected and correlations are produced with corresponding degrees of freedom of the measuring macroscopic device. These correlations are described, in the present paper, by using the Schmidt decomposition, in which the eigenvalues of the reduced density matrices of these two systems are equal. The measurement process is related to the trace operation over the observable degrees of freedom, since we do not directly measure the microscopic system but its corresponding macroscopic part in the Schmidt decomposition. This trace operation leads only to partial information on the microscopic system referred to as the "collapse" of the wave function. This interpretation is demonstrated by analyzing Stern-Gerlach experiments. (C) 2001 MAIK "Nauka/Interperiodica".