Statistical theory of ideal quantum measurement processes

An ideal measurement on a system S by an apparatus A is approached in a minimalist, statistical formulation of quantum mechanics, where states encode properties of ensembles. The required final state of S+A is shown to have a Gibbsian thermodynamic equilibrium form, not only for a large ensemble of runs, but also for arbitrary subensembles. This outcome is justified dynamically in quantum statistical mechanics as result of relaxation for models with suitably chosen interactions within A. The quantum ambiguity that precludes the interpretation of a mixed state in terms of physical subensembles is overcome due to a specific type of microcanonical relaxation. The resulting structure for the states describing subsets of runs affords an explanation for the standard properties of ideal measurements, in particular the uniqueness of the result for each individual run, thus offering a statistical solution to the quantum measurement problem.