The problem of statistical inference based on a partial measurement (“coarse-graining”) requires the specification of an a priori distribution. We reformulate the ordinary theory such as to encompass systematically a wide range of a priori distributions (“relative coarse-graining”). This is done in a mathematical setting which admits an interpretation in both classical probability and quantum mechanics. The formalism is illustrated in a few simple examples, such as the die whose geometrical shape is known, the spin in thermal equilibrium with an (...) unknown reservoir, and the position measurement of a one-dimensional particle. It is shown that some of the limitations of the usual theory are a consequence of the fact that it is restricted to “equidistributed” (symmetric) a priori states. (shrink)

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. (shrink)

We discuss in what sense the decay-scattering system is a minimal phenomenological theory for particle decay and resonance scattering.