Statistical inference and quantum mechanical measurement

We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result is to be interpreted as the statistically inferred state of the original system rather than the state of the system after measurement. The phenomenon of “reduction of states” appears in this light as a consequence of incomplete information rather than the physical interaction between measured system and measuring instrument.